In the computational process of very fast transient over-voltage （VFTO）, it is essen-tial to find an accurate model for a gas insulated substation. The arcing model of the disconnector is particularly important. The...In the computational process of very fast transient over-voltage （VFTO）, it is essen-tial to find an accurate model for a gas insulated substation. The arcing model of the disconnector is particularly important. The general arcing model is not able to give a good description of the arc development process. In this paper, based on the physical process of arcing and existing arc models （the exponential time-varying resistance model and the segmental arcing models）, a dy- namic arcing model is proposed, which is divided into two stages before and after the zero crossing. The dynamic arcing model combines hyperbola time-varying resistance and the Mayr model to describe the dynamic process of arcing. The present paper creates an arc model blockset upon the Matlab/Simulink software platform. Moreover for a specific 1100 kV station, VFTO is simulated in detail based on different arcing models. It is demonstrated that the dynamic arcing model can describe the physical arc process precisely and is useful for improving the accuracy of VFTO simulations.展开更多
The prompt extinction of the secondary arc is critical to the single-phase reclosing of AC transmission lines, including half-wavelength power transmission lines. In this paper, a low- voltage physical experimental pl...The prompt extinction of the secondary arc is critical to the single-phase reclosing of AC transmission lines, including half-wavelength power transmission lines. In this paper, a low- voltage physical experimental platform was established and the motion process of the secondary arc was recorded by a high-speed camera. It was found that the arcing time of the secondary arc rendered a close relationship with its arc length. Through the input and output power energy analysis of the secondary arc, a new critical length criterion for the arcing time was proposed. The arc chain model was then adopted to calculate the arcing time with both the traditional and the proposed critical length criteria, and the simulation results were compared with the experimental data. The study showed that the arcing time calculated from the new critical length criterion gave more accurate results, which can provide a reliable criterion in term of arcing time for modeling and simulation of the secondary arc related with power transmission lines.展开更多
A numerical simulation model for 252 kV puffer circuit breaker is constructed, by using a proven commercial computational fluid dynamics （CFD） package, PHOENICS. The model takes into account the moving parts in the ...A numerical simulation model for 252 kV puffer circuit breaker is constructed, by using a proven commercial computational fluid dynamics （CFD） package, PHOENICS. The model takes into account the moving parts in the circuit breaker, turbulence enhanced momentum and energy transport, radiation transport. The arcing process in a SF6 puffer circuit breaker with two hollow contacts is simulated under different conditions, and the simulation results are verified with experimental results. Through simulation, the pressure, temperature and velocity in the arc quenching chamber can be obtained. The simulation model is also capable of predicting the influence of design parameters variations on breaker performance, and can thus help to reduce the number of short-circuit tests during the design stage.展开更多
The dynamic physical characteristics of a DC arc on an arcing horn for a high voltage direct current(HVDC)grounding electrode line are significantly different from those of the switching device arc,secondary arc,AC fa...The dynamic physical characteristics of a DC arc on an arcing horn for a high voltage direct current(HVDC)grounding electrode line are significantly different from those of the switching device arc,secondary arc,AC fault arc and pantograph-catenary arc.In this work,an experimental platform for the DC arc on the arcing horn was built,and mechanisms of the arc column short circuit and arc root movement were studied.This work further analyzes the characteristics and mechanisms of the arc motion when wind speed and direction,magnetic field and the expansion angle of the electrode are varied.Arc root movement is more likely to occur at the upper electrode.There is a competitive relationship between arc expansion and the transferring effect.The effect of wind on the arc column is greater than the effect on the arc root.The magnetic field has a significant driving effect on both the arc column and the arc root.The research results provide a comprehensive experimental basis for forther probing the method of DC arc suppression,and the improvement of the arcing horn.展开更多
For high-voltage direct current(HVDC)power grid transmission with higher voltages,the energyconsuming branch of the DC circuit breaker is required to dissipate huge energies of more than megajoules in a short time in ...For high-voltage direct current(HVDC)power grid transmission with higher voltages,the energyconsuming branch of the DC circuit breaker is required to dissipate huge energies of more than megajoules in a short time in the case of a fault and short circuit.The requirements for huge volume and weight are difficult to meet with energy-consuming equipment based on ZnO.In this paper,a new energy consumption method is proposed based on gallium indium tin(GaInSn)liquid metal in the arcing process,and a test platform with adjustable short-circuit current is built.The mechanism triggering GaInSn liquid metal arcing energy consumption is studied.It is found that short-circuit current and channel aperture are the key parameters affecting the energy consumption of liquid metal arcing.The characteristics of GaInSn liquid metal energy consumption are investigated,and four stages of liquid metal energy consumption are found:oscillatory shrinkage,arc breakdown,arc burning phase change and arc extinction.The influence of short-circuit current and channel aperture on the energy consumption characteristics of GaInSn liquid metal is investigated.To further explore the physical mechanism of the above phenomena,a magneto-hydrodynamic model of energy consumption in the GaInSn liquid metal arcing process is established.The influence of short-circuit current and channel aperture on the temperature distribution of the liquid metal arc is analyzed.The mechanism of the effect of short-circuit current and channel aperture on peak arc temperature and the temperature diffusion rate is clarified.The research results provide theoretical support for this new liquid metal energy consumption mode DC circuit breaker.展开更多
Internal arcs cause a rapid increase in pressure in electrical installations. The type of insulation gas has influence on pressure development. Typically SF6 is used incompact metal-clad switchgear, however, it has a ...Internal arcs cause a rapid increase in pressure in electrical installations. The type of insulation gas has influence on pressure development. Typically SF6 is used incompact metal-clad switchgear, however, it has a high global warming potential. Because of this, the replacement of SF6 by alternative gases such as CO2 is under discussion. The pressure developments in a closed vessel filled with air, SF6 and CO2 are measured and compared. During internal arcing in gas-insulated switchgear, overpressure causes a rupture of a burst plate and hot gas escapes into the surrounding room mixing with air. In order to predict the pressure development in electrical installations reliably, the portion of energy causing pressure rise, arc voltage as well as reliable gas data i.e., thermodynamic and transport properties, must be known in a wide range of pressure and temperature. These data are up to now not available for CO2/air mixtures. The thermodynamic properties are directly calculated from the number densities, internal partition functions and enthalpies of formation. The transport coefficients are deduced using the Chapman-Enskog method. Comparing measured and calculated pressure developments in a test arrangement demonstrates the quality of the calculation approach.展开更多
The nozzle ablation process is described as two phases of heat and ablation in the interruption for an SF6 circuit breaker in this paper. Their mathematical models are established with the Fourier heat conduction diff...The nozzle ablation process is described as two phases of heat and ablation in the interruption for an SF6 circuit breaker in this paper. Their mathematical models are established with the Fourier heat conduction differential equation respectively. The masses of nozzle ablation with different arc durations and arc currents are calculated through the model of the nozzle abla- tion combined with an MHD （magneto-hydrodynamic） arc model. The time of the temperature rise on the inner surface of the nozzle under a given energy flux and of reaching the pyrolysis temperature under different energy fluxes is respectively analyzed. The relations between the mass of nozzle ablation and breaking current and arc duration are obtained. The result shows that the absorbing energy process before the nozzle ablation can be neglected under the condition of the energy flux entering into nozzle q 〉 10^9 W/m^2. The ablation is the severest during the high-current phase and the ablation mass increases rapidly with the breaking current and with arc duration respectively.展开更多
Graphite electrodes were used for the direct current （DC） arc discharge in water. And high-resolution transmission electron microscopy （HRTEM） was used to investigate the products. Based on the experimental phenom...Graphite electrodes were used for the direct current （DC） arc discharge in water. And high-resolution transmission electron microscopy （HRTEM） was used to investigate the products. Based on the experimental phenomena and nano-structure products, arc plasma characteristics in water were analyzed theoretically. Two growth regions and relevant growth modes were proposed to interpret the formation mechanisms of nano-structures by arc discharge in water. Furthermore, liquid nitrogen and cross magnetic field was applied to change the arcing state respectively, and new carbon nano-structures were obtained. Their formation mechanisms were also analyzed correspondingly.展开更多
Catch arc is the bottleneck of train acceleration. The arc characteristics of pantograph is an important index of the current high-speed train problems, which will seriously affect the normal operation of traction dri...Catch arc is the bottleneck of train acceleration. The arc characteristics of pantograph is an important index of the current high-speed train problems, which will seriously affect the normal operation of traction drive system. The study of the characteristics of the pantograph arc in the process of off-line pantograph can provide some help for improving the quality of the current receiving and the safe operation of the train.展开更多
Perfluoroisobutyronitrile(C_(4)F_(7)N)and its mixed gas are being widely studied as one of the most potential gases to replace SF_(6).Focusing on the breaking process of ring main unit(RMU)filled with C_(4)F_(7)N/CO_(...Perfluoroisobutyronitrile(C_(4)F_(7)N)and its mixed gas are being widely studied as one of the most potential gases to replace SF_(6).Focusing on the breaking process of ring main unit(RMU)filled with C_(4)F_(7)N/CO_(2)mixed gas under slightly positive pressure,the phase-controlled technology is used to improve the breaking capacity of the interrupter in this paper.The decomposition and consumption of C_(4)F_(7)N caused by arcing can be suppressed.Whole process arc model describing the arcing stage and current zero stage is established based on magnetohydrodynamics(MHD)and black box model(BBM).During the opening process,in which both the current and the opening distance are time-varying,influences of the arcing time on internal and external characteristics of the arc,current zero characteristics and post-arc re-ignition characteristics are theoretically analyzed.Reasonable phase-controlled arcing range(PCAR)is calculated and evaluated.According to IEC 62271-103:2011 and GB/T 3804-2017 standard,synthesis tests are carried out under different arcing times.Results show evaluated PCAR can improve characteristics of the arcing stage and reduce average arcing time.Probability of successful breaking is increased.Effectiveness of phase-controlled technology and evaluation method of arcing range under slightly positive pressure is further verified.展开更多
Medium voltage distribution networks usually suffer from single-ground arcing fault,especially high impedance arcing fault.Moreover,induced intermittent arcing faults can severely endanger the reliability and safety o...Medium voltage distribution networks usually suffer from single-ground arcing fault,especially high impedance arcing fault.Moreover,induced intermittent arcing faults can severely endanger the reliability and safety of power systems.The arc model is important for high impedance arcing fault suppression and detection to effectively eliminate the single-ground arcing fault.This paper proposes an improved arc model,which is concise and explicit,based on a single-ground arcing fault conducted on a 10 kV experimental platform under different fault conditions.Characteristic parameters of single-ground arcing faults are obtained based on test results.Furthermore,characteristic parameters under different fault conditions of the improved arc model are presented.Finally,verification of the improved arc model is supported by PSCAD-EMTDC.Comparisons of the proposed arc model between three typical black-box arc models indicate that the proposed model has better performance and higher accuracy than that of the three typical arc models as fault resistance is in a range of 0.1 kΩto 2.4 kΩ.Thus,its accuracy is acceptable and it is helpful to the simulation and suppression of arc fault overvoltage.展开更多
Wire arc additive manufacturing(WAAM)has emerged as a promising approach for fabricating large-scale components.However,conventional WAAM still faces challenges in optimizing microstructural evolution,minimizing addit...Wire arc additive manufacturing(WAAM)has emerged as a promising approach for fabricating large-scale components.However,conventional WAAM still faces challenges in optimizing microstructural evolution,minimizing additive-induced defects,and alleviating residual stress and deformation,all of which are critical for enhancing the mechanical performance of the manufactured parts.Integrating interlayer friction stir processing(FSP)into WAAM significantly enhances the quality of deposited materials.However,numerical simulation research focusing on elucidating the associated thermomechanical coupling mechanisms remains insufficient.A comprehensive numerical model was developed to simulate the thermomechanical coupling behavior in friction stir-assisted WAAM.The influence of post-deposition FSP on the coupled thermomechanical response of the WAAM process was analyzed quantitatively.Moreover,the residual stress distribution and deformation behavior under both single-layer and multilayer deposition conditions were investigated.Thermal analysis of different deposition layers in WAAM and friction stir-assisted WAAM was conducted.Results show that subsequent layer deposition induces partial remelting of the previously solidified layer,whereas FSP does not cause such remelting.Furthermore,thermal stress and deformation analysis confirm that interlayer FSP effectively mitigates residual stresses and distortion in WAAM components,thereby improving their structural integrity and mechanical properties.展开更多
A tournament is an orientation of the edges of a complete graph.An arc in a digraph D is pancyclic if it is contained in a cycle of length k for every 3≤k≤|V(D)|.An arc uv in a digraph D is k-anticyclic if there is ...A tournament is an orientation of the edges of a complete graph.An arc in a digraph D is pancyclic if it is contained in a cycle of length k for every 3≤k≤|V(D)|.An arc uv in a digraph D is k-anticyclic if there is a path from u to v of length k-1 in D.If for every3≤k≤|V(D)|,an arc uv is k-anticyclic,then we say that uv is anti-pancyclic in D.It has been proved in Discrete Appl.Math.79(1997)127-135 that every arc of a 3-strong and arc-3-cyclic tournament T is k-anticyclic for each k≥4,unless T is isomorphic to two tournaments,each of which has exactly 8 vertices.In J.Combin.Inform.System Sci.19(1994)207-214,Moon showed that every strong tournament contains at least three pancyclic arcs and characterized the tournaments that attain this lower bound.In this paper we investigate the number of antipancyclic arcs in strong tournaments and show that every strong tournament with order n≥6contains at least four anti-pancyclic arcs unless it is isomorphic to five tournaments,each of which has exactly 6 vertices.Consequently,every strong tournament with order n≥7 contains at least four anti-pancyclic arcs.展开更多
基金supported by Special Research Fund for Doctoral Program of Education Ministry of China (No. 20092102110001)Natural Science Foundation of Liaoning Province of China (No. 201102169)National Natural Science Foundation of China (No. 51277123)
文摘In the computational process of very fast transient over-voltage （VFTO）, it is essen-tial to find an accurate model for a gas insulated substation. The arcing model of the disconnector is particularly important. The general arcing model is not able to give a good description of the arc development process. In this paper, based on the physical process of arcing and existing arc models （the exponential time-varying resistance model and the segmental arcing models）, a dy- namic arcing model is proposed, which is divided into two stages before and after the zero crossing. The dynamic arcing model combines hyperbola time-varying resistance and the Mayr model to describe the dynamic process of arcing. The present paper creates an arc model blockset upon the Matlab/Simulink software platform. Moreover for a specific 1100 kV station, VFTO is simulated in detail based on different arcing models. It is demonstrated that the dynamic arcing model can describe the physical arc process precisely and is useful for improving the accuracy of VFTO simulations.
基金supported by National Natural Science Foundation of China(Nos.51277061 and 51420105011)
文摘The prompt extinction of the secondary arc is critical to the single-phase reclosing of AC transmission lines, including half-wavelength power transmission lines. In this paper, a low- voltage physical experimental platform was established and the motion process of the secondary arc was recorded by a high-speed camera. It was found that the arcing time of the secondary arc rendered a close relationship with its arc length. Through the input and output power energy analysis of the secondary arc, a new critical length criterion for the arcing time was proposed. The arc chain model was then adopted to calculate the arcing time with both the traditional and the proposed critical length criteria, and the simulation results were compared with the experimental data. The study showed that the arcing time calculated from the new critical length criterion gave more accurate results, which can provide a reliable criterion in term of arcing time for modeling and simulation of the secondary arc related with power transmission lines.
文摘A numerical simulation model for 252 kV puffer circuit breaker is constructed, by using a proven commercial computational fluid dynamics （CFD） package, PHOENICS. The model takes into account the moving parts in the circuit breaker, turbulence enhanced momentum and energy transport, radiation transport. The arcing process in a SF6 puffer circuit breaker with two hollow contacts is simulated under different conditions, and the simulation results are verified with experimental results. Through simulation, the pressure, temperature and velocity in the arc quenching chamber can be obtained. The simulation model is also capable of predicting the influence of design parameters variations on breaker performance, and can thus help to reduce the number of short-circuit tests during the design stage.
基金National Natural Science Foundation of China(No.51907168)funded by Sichuan Science and Technology Program(Outstanding Youth Science and Technology Talents)(No.2020JDJQ0039)。
文摘The dynamic physical characteristics of a DC arc on an arcing horn for a high voltage direct current(HVDC)grounding electrode line are significantly different from those of the switching device arc,secondary arc,AC fault arc and pantograph-catenary arc.In this work,an experimental platform for the DC arc on the arcing horn was built,and mechanisms of the arc column short circuit and arc root movement were studied.This work further analyzes the characteristics and mechanisms of the arc motion when wind speed and direction,magnetic field and the expansion angle of the electrode are varied.Arc root movement is more likely to occur at the upper electrode.There is a competitive relationship between arc expansion and the transferring effect.The effect of wind on the arc column is greater than the effect on the arc root.The magnetic field has a significant driving effect on both the arc column and the arc root.The research results provide a comprehensive experimental basis for forther probing the method of DC arc suppression,and the improvement of the arcing horn.
基金supported by National Natural Science Foundation of China(No.U1966602)the Excellent Young Scientists Fund of China(No.51922090).
文摘For high-voltage direct current(HVDC)power grid transmission with higher voltages,the energyconsuming branch of the DC circuit breaker is required to dissipate huge energies of more than megajoules in a short time in the case of a fault and short circuit.The requirements for huge volume and weight are difficult to meet with energy-consuming equipment based on ZnO.In this paper,a new energy consumption method is proposed based on gallium indium tin(GaInSn)liquid metal in the arcing process,and a test platform with adjustable short-circuit current is built.The mechanism triggering GaInSn liquid metal arcing energy consumption is studied.It is found that short-circuit current and channel aperture are the key parameters affecting the energy consumption of liquid metal arcing.The characteristics of GaInSn liquid metal energy consumption are investigated,and four stages of liquid metal energy consumption are found:oscillatory shrinkage,arc breakdown,arc burning phase change and arc extinction.The influence of short-circuit current and channel aperture on the energy consumption characteristics of GaInSn liquid metal is investigated.To further explore the physical mechanism of the above phenomena,a magneto-hydrodynamic model of energy consumption in the GaInSn liquid metal arcing process is established.The influence of short-circuit current and channel aperture on the temperature distribution of the liquid metal arc is analyzed.The mechanism of the effect of short-circuit current and channel aperture on peak arc temperature and the temperature diffusion rate is clarified.The research results provide theoretical support for this new liquid metal energy consumption mode DC circuit breaker.
文摘Internal arcs cause a rapid increase in pressure in electrical installations. The type of insulation gas has influence on pressure development. Typically SF6 is used incompact metal-clad switchgear, however, it has a high global warming potential. Because of this, the replacement of SF6 by alternative gases such as CO2 is under discussion. The pressure developments in a closed vessel filled with air, SF6 and CO2 are measured and compared. During internal arcing in gas-insulated switchgear, overpressure causes a rupture of a burst plate and hot gas escapes into the surrounding room mixing with air. In order to predict the pressure development in electrical installations reliably, the portion of energy causing pressure rise, arc voltage as well as reliable gas data i.e., thermodynamic and transport properties, must be known in a wide range of pressure and temperature. These data are up to now not available for CO2/air mixtures. The thermodynamic properties are directly calculated from the number densities, internal partition functions and enthalpies of formation. The transport coefficients are deduced using the Chapman-Enskog method. Comparing measured and calculated pressure developments in a test arrangement demonstrates the quality of the calculation approach.
基金supported by National Natural Science Foundation of China(Nos.51177005 and 51477004)
文摘The nozzle ablation process is described as two phases of heat and ablation in the interruption for an SF6 circuit breaker in this paper. Their mathematical models are established with the Fourier heat conduction differential equation respectively. The masses of nozzle ablation with different arc durations and arc currents are calculated through the model of the nozzle abla- tion combined with an MHD （magneto-hydrodynamic） arc model. The time of the temperature rise on the inner surface of the nozzle under a given energy flux and of reaching the pyrolysis temperature under different energy fluxes is respectively analyzed. The relations between the mass of nozzle ablation and breaking current and arc duration are obtained. The result shows that the absorbing energy process before the nozzle ablation can be neglected under the condition of the energy flux entering into nozzle q 〉 10^9 W/m^2. The ablation is the severest during the high-current phase and the ablation mass increases rapidly with the breaking current and with arc duration respectively.
基金National Natural Science Foundation of China (No.50377030)
文摘Graphite electrodes were used for the direct current （DC） arc discharge in water. And high-resolution transmission electron microscopy （HRTEM） was used to investigate the products. Based on the experimental phenomena and nano-structure products, arc plasma characteristics in water were analyzed theoretically. Two growth regions and relevant growth modes were proposed to interpret the formation mechanisms of nano-structures by arc discharge in water. Furthermore, liquid nitrogen and cross magnetic field was applied to change the arcing state respectively, and new carbon nano-structures were obtained. Their formation mechanisms were also analyzed correspondingly.
文摘Catch arc is the bottleneck of train acceleration. The arc characteristics of pantograph is an important index of the current high-speed train problems, which will seriously affect the normal operation of traction drive system. The study of the characteristics of the pantograph arc in the process of off-line pantograph can provide some help for improving the quality of the current receiving and the safe operation of the train.
基金supported by National Natural Science Foundation of China(51977022)。
文摘Perfluoroisobutyronitrile(C_(4)F_(7)N)and its mixed gas are being widely studied as one of the most potential gases to replace SF_(6).Focusing on the breaking process of ring main unit(RMU)filled with C_(4)F_(7)N/CO_(2)mixed gas under slightly positive pressure,the phase-controlled technology is used to improve the breaking capacity of the interrupter in this paper.The decomposition and consumption of C_(4)F_(7)N caused by arcing can be suppressed.Whole process arc model describing the arcing stage and current zero stage is established based on magnetohydrodynamics(MHD)and black box model(BBM).During the opening process,in which both the current and the opening distance are time-varying,influences of the arcing time on internal and external characteristics of the arc,current zero characteristics and post-arc re-ignition characteristics are theoretically analyzed.Reasonable phase-controlled arcing range(PCAR)is calculated and evaluated.According to IEC 62271-103:2011 and GB/T 3804-2017 standard,synthesis tests are carried out under different arcing times.Results show evaluated PCAR can improve characteristics of the arcing stage and reduce average arcing time.Probability of successful breaking is increased.Effectiveness of phase-controlled technology and evaluation method of arcing range under slightly positive pressure is further verified.
基金supported by National Natural Science Foundation of China under Grant No.51477018 and No.52077019。
文摘Medium voltage distribution networks usually suffer from single-ground arcing fault,especially high impedance arcing fault.Moreover,induced intermittent arcing faults can severely endanger the reliability and safety of power systems.The arc model is important for high impedance arcing fault suppression and detection to effectively eliminate the single-ground arcing fault.This paper proposes an improved arc model,which is concise and explicit,based on a single-ground arcing fault conducted on a 10 kV experimental platform under different fault conditions.Characteristic parameters of single-ground arcing faults are obtained based on test results.Furthermore,characteristic parameters under different fault conditions of the improved arc model are presented.Finally,verification of the improved arc model is supported by PSCAD-EMTDC.Comparisons of the proposed arc model between three typical black-box arc models indicate that the proposed model has better performance and higher accuracy than that of the three typical arc models as fault resistance is in a range of 0.1 kΩto 2.4 kΩ.Thus,its accuracy is acceptable and it is helpful to the simulation and suppression of arc fault overvoltage.
基金National Key Research and Development Program of China(2022YFB4600902)Shandong Provincial Science Foundation for Outstanding Young Scholars(ZR2024YQ020)。
文摘Wire arc additive manufacturing(WAAM)has emerged as a promising approach for fabricating large-scale components.However,conventional WAAM still faces challenges in optimizing microstructural evolution,minimizing additive-induced defects,and alleviating residual stress and deformation,all of which are critical for enhancing the mechanical performance of the manufactured parts.Integrating interlayer friction stir processing(FSP)into WAAM significantly enhances the quality of deposited materials.However,numerical simulation research focusing on elucidating the associated thermomechanical coupling mechanisms remains insufficient.A comprehensive numerical model was developed to simulate the thermomechanical coupling behavior in friction stir-assisted WAAM.The influence of post-deposition FSP on the coupled thermomechanical response of the WAAM process was analyzed quantitatively.Moreover,the residual stress distribution and deformation behavior under both single-layer and multilayer deposition conditions were investigated.Thermal analysis of different deposition layers in WAAM and friction stir-assisted WAAM was conducted.Results show that subsequent layer deposition induces partial remelting of the previously solidified layer,whereas FSP does not cause such remelting.Furthermore,thermal stress and deformation analysis confirm that interlayer FSP effectively mitigates residual stresses and distortion in WAAM components,thereby improving their structural integrity and mechanical properties.
基金Supported by the National Natural Sciences Foundation for Young Scientists of China(11701349)the Natural Science Foundation of Shanxi Province,China(202203021211318,202103021224019)。
文摘A tournament is an orientation of the edges of a complete graph.An arc in a digraph D is pancyclic if it is contained in a cycle of length k for every 3≤k≤|V(D)|.An arc uv in a digraph D is k-anticyclic if there is a path from u to v of length k-1 in D.If for every3≤k≤|V(D)|,an arc uv is k-anticyclic,then we say that uv is anti-pancyclic in D.It has been proved in Discrete Appl.Math.79(1997)127-135 that every arc of a 3-strong and arc-3-cyclic tournament T is k-anticyclic for each k≥4,unless T is isomorphic to two tournaments,each of which has exactly 8 vertices.In J.Combin.Inform.System Sci.19(1994)207-214,Moon showed that every strong tournament contains at least three pancyclic arcs and characterized the tournaments that attain this lower bound.In this paper we investigate the number of antipancyclic arcs in strong tournaments and show that every strong tournament with order n≥6contains at least four anti-pancyclic arcs unless it is isomorphic to five tournaments,each of which has exactly 6 vertices.Consequently,every strong tournament with order n≥7 contains at least four anti-pancyclic arcs.
