In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that...Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.展开更多
By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative egect to K-factor of the Drell-Yan process is numerically investigated for 6^...By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative egect to K-factor of the Drell-Yan process is numerically investigated for 6^12C- 6^12C collision at the center-of-mass energy √s- 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.展开更多
In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of ...In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.展开更多
The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This stud...The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This study was carried out over the city of Lokoja,Nigeria,using ten years(2011 to 2020)atmospheric data of temperature,pressure and humidity both at the surface(12 m)and at 100 m AGL.The data were retrieved from European Centre for Medium-Range Weather Forecasts(ECMWF)ERA5.The k-factor yearly variation follows the same trend with minimum and maximum values obtained during dry and wet season months respectively.In addition,the highest mean value of 1.00042 was recorded in the month of August while the lowest value of 1.00040 was recorded in the month of January with an overall mean value of 1.0003.This value is less than the recommended standard of 1.33 by ITU-R.The propagation effect corresponding to k<1.33 is sub-refractive.The implication of this on radio wave propagation,especially terrestrial communications is that transmitted wireless signal is prone to losses.This can be mitigated through an effective power budget:Choice of transmitting antenna’s height and gain,so as to improve the Quality of Service over the study area.展开更多
The prevalence of unwholesome land use practices and population pressure exacerbates soil loss which is worsening the problem of sedimentation of the Kubanni dam. This study was conducted at the Kubanni drainage basin...The prevalence of unwholesome land use practices and population pressure exacerbates soil loss which is worsening the problem of sedimentation of the Kubanni dam. This study was conducted at the Kubanni drainage basin covering a spatial area of 56.7 Km2 in Samaru, Zaria, Nigeria to estimate annual soil loss using the RUSLE model. Satellite images of Landsat OLI for December 2014, 2016, 2018, February, July and November 2022;soil data, rainfall data from 2010 to 2022, and DEM of 30-meter resolution were utilized for the study. All factors of the RUSLE model were calculated for the basin using assembled data. The erosivity (R-factor) was discovered to be 553.437 MJ∙mm∙ha−1∙h−1∙yr−1. The average erodibility (K-factor) value was 0.1 Mg∙h∙h∙ha−1∙MJ−1∙mm−1∙yr−1. The Slope Length and Steepness factor (LS-factor) in the basin ranged between 0% and 13.47%. The Crop Management Factor (C-factor) values were obtained from a rescaling of the NDVI values derived for the study area and ranged from 0.26 to 0.55. Support practice (P-factors) were computed from the prevalent tillage practice in the basin and ranged from 0.27 to 0.40. The soil loss amount for the Kubanni basin was found to be 28441.482 tons∙ha−1∙yr−1, while the annual soil loss for the entire Kubanni drainage basin was found to be 49780.257 tons∙yr−1. The study has demonstrated the viability of coupling RUSLE model and Remote Sensing and Geographic Information System (GIS) techniques for the estimation of soil loss in the Kubanni drainage basin.展开更多
In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime numbe...In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.展开更多
A k-regular spanning subgraph of graph G is called a k-factor of G. Graph G is called a k-deleted graph if G-e has a k-factor for each edge e. A graph G=(X,Y) with bipartition (X,Y) is called a bipartite graph if ever...A k-regular spanning subgraph of graph G is called a k-factor of G. Graph G is called a k-deleted graph if G-e has a k-factor for each edge e. A graph G=(X,Y) with bipartition (X,Y) is called a bipartite graph if every edge of G has one endpoint in X and the other in Y.It is proved that a bipartite graph G=(X,Y) with X=Y is a k-deleted graph if and only if kS≤r 1+2r 2+...+k(r k+...+r Δ)-ε(S) for all SX. Using this result we give a sufficient neighborhood condition for a bipartite to be a k-deleted graph.展开更多
In order to obtain accurate characteristics of wireless channels in the viaduct area of China, a channel meas- urement was taken in a railway viaduct scenario of the Zhengzhou-Xi＇an passenger dedicated line with a ba...In order to obtain accurate characteristics of wireless channels in the viaduct area of China, a channel meas- urement was taken in a railway viaduct scenario of the Zhengzhou-Xi＇an passenger dedicated line with a bandwidth of 50 MHz at 2.35 GHz. The single-slope log-distance model is used to analyze the path-loss （PL）, and the distribution of shadow fading （SF） is obtained by statistical methods, which shows that the normal distribution fits the samples well. Ricean K-factor is analyzed by the method of moments, and the variation of K-factor is given along the measured route. Small scale such as delay spread and Doppler behavior are parameterized. Based on empirical channel measurement, this paper provides parameters for the evaluation and simulation work on viaduct scenarios of high-speed railway.展开更多
Soil erosion in mountain rangelands in Kyrgyzstan is an emerging problem due to vegetation loss caused by overgrazing. It is further exacerbated by mountain terrain and high precipitation values in Fergana range in th...Soil erosion in mountain rangelands in Kyrgyzstan is an emerging problem due to vegetation loss caused by overgrazing. It is further exacerbated by mountain terrain and high precipitation values in Fergana range in the south of Kyrgyzstan. The main objective of this study was to map soil erodibility in the mountainous rangelands of Kyrgyzstan. The results of this effort are expected to contribute to the development of soil erodibility modelling approaches for mountainous areas. In this study, we mapped soil erodibility at two sites, both representing grazing rangelands in the mountains of Kyrgyzstan and having potentially different levels of grazing pressure. We collected a total of 232 soil samples evenly distributed in geographical space and feature space. Then we analyzed the samples in laboratory for grain size distribution and calculated soil erodibility values from these data using the Revised Universal Soil Loss Equation (RUSLE) K-factor formula. After that, we derived different terrain indices and ratios of frequency bands from ASTER GDEM and LANDSAT images to use as auxiliary data because they are among the main soil forming factors and widely used for prediction of various soil properties. Soil erodibility was significantly correlated with channel network base level (geographically extrapolated altitude of water channels), remotely sensed indices of short-wave infrared spectral bands, exposition, and slope degree. We applied multiple regression analysis to predict soil erodibility from spatially explicit terrain and remotely sensed indices. The final soil erodibility model was developed using the spatially explicit predictors and the regression equation and then improved by adding the residuals. The spatial resolution of the model was 30 m, and the estimated mean adjusted coefficient of determination was 0.47. The two sites indicated different estimated and predicted means of soil erodibility values (0.035 and 0.039) with a 0.05 significance level, which is attributed mainly to the considerable difference in elevation.展开更多
A consistent approach to estimating nuclear effect functions RA RvA (x2) and RSA(x2) based on numerical iteration technique is presented in the quark-parton model when taking into account the nonconstancy of quantum c...A consistent approach to estimating nuclear effect functions RA RvA (x2) and RSA(x2) based on numerical iteration technique is presented in the quark-parton model when taking into account the nonconstancy of quantum chromodynamics correction factor K. ARv (x2) and RsA(x2) correspond respectively to the valence quark distributions for one bound nucleon within the nucleus and to the sea quark ones. Related numerical analysis is given for nuclei 6 12C,20 40Ca, and 26 56Fe. As the basis, it adopts both experimental data of the high energy proton-nucleus Drell-Yan process and of the high energy lepton-nucleus deep inelastic scattering.展开更多
In this paper, diversity-multiplexing tradeoff (DMT) curve for 2×2 Dual-Polarized uncorrelated Rice MIMO channels is studied. Exact expressions for statistic information of mutual information exponent are derived...In this paper, diversity-multiplexing tradeoff (DMT) curve for 2×2 Dual-Polarized uncorrelated Rice MIMO channels is studied. Exact expressions for statistic information of mutual information exponent are derived. Impacts of channel parameters such as signal to noise ratio (SNR), k-factor and cross polarization discrimination (XPD) on mutual information exponent are analyzed. Compared to conventional single-polarized (SP) Rice MIMO systems, a qualitatively different behavior is observed for DP Rice systems. The work in this paper, allows identifying quantitatively for which channels (k-factor) and SNR levels the use of dual polarization becomes beneficial. Gamma or lognormal distribution are used to describe mutual information component, and a theoretical formulation for finite-SNR DMT curve in 2×2 DP uncorrelated Rice channels is presented for the first time, which is valid in low and medium SNRs when multiplexing gain is larger than 0.75.展开更多
A graph G is a fractional(k,m)-deleted graph if removing any m edges from G,the resulting subgraph still admits a fractional k-factor.Let k≥2 and m≥1 be integers.Denote[2m/k]^(*)=[2m/k]if 2m/k is not an integer,and[...A graph G is a fractional(k,m)-deleted graph if removing any m edges from G,the resulting subgraph still admits a fractional k-factor.Let k≥2 and m≥1 be integers.Denote[2m/k]^(*)=[2m/k]if 2m/k is not an integer,and[2m/k]^(*)=[2m/k]-1 if 2m/k is an integer.In this paper,we prove that G is a fractional(k,m)-deleted graph if δ(G)≥k+m and isolated toughness meets I(G)>{3-1/m,if k=2 and m≥3,k+[2m/k]^(*)m+1-[2m/k]^(*);otherwise.Furthermore,we show that the isolated toughness bound is tight.展开更多
Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I o...Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.展开更多
We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Ja...We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Jachson, respectively.展开更多
Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e...Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.展开更多
A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G b...A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G be an n/2-critical graph of even order n≥8k-14.It is shown in this paper that for any given Hamiltonian cycle C except that G-C consists of two components of odd orders when k is odd,G has a k-factor containing C.展开更多
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
基金Supported by National Natural Science Foundation of China.
文摘Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.
基金The project supported by the Natural Science Foundation of Hebei Province of China under Grant No, A2005000535
文摘By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative egect to K-factor of the Drell-Yan process is numerically investigated for 6^12C- 6^12C collision at the center-of-mass energy √s- 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.
基金This work is supported by NSFC (10471078.10201019)RSDP (20040422004) of China
文摘In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.
文摘The effective earth radius factor(k-factor)has a refractive propagation effect on transmitted radio signals thus making its study necessary for the proper planning of terrestrial radio links and power budget.This study was carried out over the city of Lokoja,Nigeria,using ten years(2011 to 2020)atmospheric data of temperature,pressure and humidity both at the surface(12 m)and at 100 m AGL.The data were retrieved from European Centre for Medium-Range Weather Forecasts(ECMWF)ERA5.The k-factor yearly variation follows the same trend with minimum and maximum values obtained during dry and wet season months respectively.In addition,the highest mean value of 1.00042 was recorded in the month of August while the lowest value of 1.00040 was recorded in the month of January with an overall mean value of 1.0003.This value is less than the recommended standard of 1.33 by ITU-R.The propagation effect corresponding to k<1.33 is sub-refractive.The implication of this on radio wave propagation,especially terrestrial communications is that transmitted wireless signal is prone to losses.This can be mitigated through an effective power budget:Choice of transmitting antenna’s height and gain,so as to improve the Quality of Service over the study area.
文摘The prevalence of unwholesome land use practices and population pressure exacerbates soil loss which is worsening the problem of sedimentation of the Kubanni dam. This study was conducted at the Kubanni drainage basin covering a spatial area of 56.7 Km2 in Samaru, Zaria, Nigeria to estimate annual soil loss using the RUSLE model. Satellite images of Landsat OLI for December 2014, 2016, 2018, February, July and November 2022;soil data, rainfall data from 2010 to 2022, and DEM of 30-meter resolution were utilized for the study. All factors of the RUSLE model were calculated for the basin using assembled data. The erosivity (R-factor) was discovered to be 553.437 MJ∙mm∙ha−1∙h−1∙yr−1. The average erodibility (K-factor) value was 0.1 Mg∙h∙h∙ha−1∙MJ−1∙mm−1∙yr−1. The Slope Length and Steepness factor (LS-factor) in the basin ranged between 0% and 13.47%. The Crop Management Factor (C-factor) values were obtained from a rescaling of the NDVI values derived for the study area and ranged from 0.26 to 0.55. Support practice (P-factors) were computed from the prevalent tillage practice in the basin and ranged from 0.27 to 0.40. The soil loss amount for the Kubanni basin was found to be 28441.482 tons∙ha−1∙yr−1, while the annual soil loss for the entire Kubanni drainage basin was found to be 49780.257 tons∙yr−1. The study has demonstrated the viability of coupling RUSLE model and Remote Sensing and Geographic Information System (GIS) techniques for the estimation of soil loss in the Kubanni drainage basin.
文摘In this paper, a necessary condition for a bipartite graph λK m,n to be K 1,k factorizable and a sufficient condition for kK m,n to have a K 1,k factorization whenever k is a prime number are given.
文摘A k-regular spanning subgraph of graph G is called a k-factor of G. Graph G is called a k-deleted graph if G-e has a k-factor for each edge e. A graph G=(X,Y) with bipartition (X,Y) is called a bipartite graph if every edge of G has one endpoint in X and the other in Y.It is proved that a bipartite graph G=(X,Y) with X=Y is a k-deleted graph if and only if kS≤r 1+2r 2+...+k(r k+...+r Δ)-ε(S) for all SX. Using this result we give a sufficient neighborhood condition for a bipartite to be a k-deleted graph.
基金supported by the National Science & Technology Pillar Program(No.2012BAF14B01)the National Natural Science Foundation of China(No.61171105)China Mobile Research Institute
文摘In order to obtain accurate characteristics of wireless channels in the viaduct area of China, a channel meas- urement was taken in a railway viaduct scenario of the Zhengzhou-Xi＇an passenger dedicated line with a bandwidth of 50 MHz at 2.35 GHz. The single-slope log-distance model is used to analyze the path-loss （PL）, and the distribution of shadow fading （SF） is obtained by statistical methods, which shows that the normal distribution fits the samples well. Ricean K-factor is analyzed by the method of moments, and the variation of K-factor is given along the measured route. Small scale such as delay spread and Doppler behavior are parameterized. Based on empirical channel measurement, this paper provides parameters for the evaluation and simulation work on viaduct scenarios of high-speed railway.
基金a part of a joint Kyrgyz-German research project “The Impact of the Transformation Process on Human-Environment Interactions in Southern Kyrgyzstan”, funded by the Volkswagen Foundation, Germany, which had no impact on research or result dissemination
文摘Soil erosion in mountain rangelands in Kyrgyzstan is an emerging problem due to vegetation loss caused by overgrazing. It is further exacerbated by mountain terrain and high precipitation values in Fergana range in the south of Kyrgyzstan. The main objective of this study was to map soil erodibility in the mountainous rangelands of Kyrgyzstan. The results of this effort are expected to contribute to the development of soil erodibility modelling approaches for mountainous areas. In this study, we mapped soil erodibility at two sites, both representing grazing rangelands in the mountains of Kyrgyzstan and having potentially different levels of grazing pressure. We collected a total of 232 soil samples evenly distributed in geographical space and feature space. Then we analyzed the samples in laboratory for grain size distribution and calculated soil erodibility values from these data using the Revised Universal Soil Loss Equation (RUSLE) K-factor formula. After that, we derived different terrain indices and ratios of frequency bands from ASTER GDEM and LANDSAT images to use as auxiliary data because they are among the main soil forming factors and widely used for prediction of various soil properties. Soil erodibility was significantly correlated with channel network base level (geographically extrapolated altitude of water channels), remotely sensed indices of short-wave infrared spectral bands, exposition, and slope degree. We applied multiple regression analysis to predict soil erodibility from spatially explicit terrain and remotely sensed indices. The final soil erodibility model was developed using the spatially explicit predictors and the regression equation and then improved by adding the residuals. The spatial resolution of the model was 30 m, and the estimated mean adjusted coefficient of determination was 0.47. The two sites indicated different estimated and predicted means of soil erodibility values (0.035 and 0.039) with a 0.05 significance level, which is attributed mainly to the considerable difference in elevation.
文摘A consistent approach to estimating nuclear effect functions RA RvA (x2) and RSA(x2) based on numerical iteration technique is presented in the quark-parton model when taking into account the nonconstancy of quantum chromodynamics correction factor K. ARv (x2) and RsA(x2) correspond respectively to the valence quark distributions for one bound nucleon within the nucleus and to the sea quark ones. Related numerical analysis is given for nuclei 6 12C,20 40Ca, and 26 56Fe. As the basis, it adopts both experimental data of the high energy proton-nucleus Drell-Yan process and of the high energy lepton-nucleus deep inelastic scattering.
文摘In this paper, diversity-multiplexing tradeoff (DMT) curve for 2×2 Dual-Polarized uncorrelated Rice MIMO channels is studied. Exact expressions for statistic information of mutual information exponent are derived. Impacts of channel parameters such as signal to noise ratio (SNR), k-factor and cross polarization discrimination (XPD) on mutual information exponent are analyzed. Compared to conventional single-polarized (SP) Rice MIMO systems, a qualitatively different behavior is observed for DP Rice systems. The work in this paper, allows identifying quantitatively for which channels (k-factor) and SNR levels the use of dual polarization becomes beneficial. Gamma or lognormal distribution are used to describe mutual information component, and a theoretical formulation for finite-SNR DMT curve in 2×2 DP uncorrelated Rice channels is presented for the first time, which is valid in low and medium SNRs when multiplexing gain is larger than 0.75.
基金supported by the National Science Foundation of China(Nos.12161094,12031018,11871270,12161141003and11931006).
文摘A graph G is a fractional(k,m)-deleted graph if removing any m edges from G,the resulting subgraph still admits a fractional k-factor.Let k≥2 and m≥1 be integers.Denote[2m/k]^(*)=[2m/k]if 2m/k is not an integer,and[2m/k]^(*)=[2m/k]-1 if 2m/k is an integer.In this paper,we prove that G is a fractional(k,m)-deleted graph if δ(G)≥k+m and isolated toughness meets I(G)>{3-1/m,if k=2 and m≥3,k+[2m/k]^(*)m+1-[2m/k]^(*);otherwise.Furthermore,we show that the isolated toughness bound is tight.
基金supported by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)+3 种基金333 Project of Jiangsu Provincethe National Social Science Foundation of China(Grant No.14AGL001)the Natural Science Foundation of Xinjiang Province of China(Grant No.2015211A003)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(Grant No.14KJD110002)
文摘Let G be a graph, and k a positive integer. A graph G is fractional independent-set-deletable k-factor-critical(in short, fractional ID-k-factor-critical) if G-I has a fractional k-factor for every independent set I of G. In this paper, we present a sufficient condition for a graph to be fractional ID-k-factor-critical,depending on the minimum degree and the neighborhoods of independent sets. Furthermore, it is shown that this result in this paper is best possible in some sense.
基金supported by the Key Laboratory of Power System,Tsinghua University
文摘We discuss k-factors and Hamiltonian Graphs in graph theory. We prove a general version of the conjecture by R. Haggkvist; as a result, we prove two extended versions of two well-known theorems due to O. Ore and B. Jachson, respectively.
基金sponsored by the National Natural Science Foundation of China(Grant No.11371009,11501256,61503160)the National Social Science Foundation of China(Grant No.11BGL039)+1 种基金Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Province
文摘Let G be a graph and k≥2 a positive integer. Let h ： E（G）→[0, 1] be a function. If e∑eЭxh（e） = k holds for each x∈V（G）, then we call G[Fh ] a fractional k-factor of G with indicator function h where Fh ={e∈E（G） ： h（e） 〉 0}. A graph G is fractional independent-set-deletable k-factor-critical（in short, fractional ID-k-factor-critical）, if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n≥9 k-14 and for any subset X？V（G） we have NG（X） = V（G） if ｜X｜ ≥ kn/（3k-1）; or ｜NG（X）3 k-1/k｜ ≥｜X｜if｜X｜〈 kn/（3k-1）,then G is fractional ID-k-factor-critical.
基金This research is supported partially by the National Natural Science Foundation of China.
文摘A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G be an n/2-critical graph of even order n≥8k-14.It is shown in this paper that for any given Hamiltonian cycle C except that G-C consists of two components of odd orders when k is odd,G has a k-factor containing C.
