For a fixed graph F,a graph G is F-saturated if it has no F as a subgraph,but does contain F after the addition of any new edge.The saturation number,sat(n,F),is the minimum number of edges of a graph in the set of al...For a fixed graph F,a graph G is F-saturated if it has no F as a subgraph,but does contain F after the addition of any new edge.The saturation number,sat(n,F),is the minimum number of edges of a graph in the set of all F-saturated graphs with order n.In this paper,we determine the saturation number sat(n,2P3∪tP2)and characterize the extremal graphs for n≥6t+8.展开更多
The k-ary n-cube Qkn （n ≥2 and k ≥3） is one of the most popular interconnection networks. In this paper, we consider the problem of a fault- free Hamiltonian cycle passing through a prescribed linear forest （i.e....The k-ary n-cube Qkn （n ≥2 and k ≥3） is one of the most popular interconnection networks. In this paper, we consider the problem of a fault- free Hamiltonian cycle passing through a prescribed linear forest （i.e., pairwise vertex-disjoint paths） in the 3-ary n-cube Qn^3 with faulty edges. The following result is obtained. Let E0 （≠θ） be a linear forest and F （≠θ） be a set of faulty edges in Q3 such that E0∩ F = 0 and ｜E0｜ ＋｜F｜ ≤ 2n - 2. Then all edges of E0 lie on a Hamiltonian cycle in Qn^3- F, and the upper bound 2n - 2 is sharp.展开更多
A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}...A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.展开更多
A linear forest is a graph consisting of paths.In this paper,the authors determine the maximum number of edges in an(m,n)-bipartite graph which does not contain a linear forest consisting of paths on at least four ver...A linear forest is a graph consisting of paths.In this paper,the authors determine the maximum number of edges in an(m,n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n≥m when m is sufficiently large.展开更多
Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edg...Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by ex,(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated vertices.Let Ln,k be the family of all linear forests of n vertices with k edges.In this paper,Turan number of Berge-Ln,in an r-uniform hypergraph is studied.When r≥k+1 and 3≤r≤l[]=1,we determine 2 the exact value of ex,(n,Berge-Ln,)respectively.When K-1≤r≤k,we 2 determine the upper bound of ex,(n,Berge-Ln,).展开更多
It is a well known fact that the linear arboricity of a k-regular graph is [(k+1)/2] fork=3,4. In this paper, we prove that if the number Of edges of a k-regular circulant is divisibleby [(k+1)/2], then its edge set c...It is a well known fact that the linear arboricity of a k-regular graph is [(k+1)/2] fork=3,4. In this paper, we prove that if the number Of edges of a k-regular circulant is divisibleby [(k+1)/2], then its edge set can be partitioned into [(k+1)/2] isomorphic linear forests, fork=3,4.展开更多
A linear forest is a forest whose components are paths. The linear arboricity la （G） of a graph G is the minimum number of linear forests which partition the edge set E（G） of G. The Cartesian product G□H of two g...A linear forest is a forest whose components are paths. The linear arboricity la （G） of a graph G is the minimum number of linear forests which partition the edge set E（G） of G. The Cartesian product G□H of two graphs G and H is defined as the graph with vertex set V（G□H） = {（u, v）｜ u ∈V（G）, v∈V（H） } and edge set E（G□H） = { （ u, x） （ v, Y）｜u=v and xy∈E（H）, or uv∈E（G） and x=y}. Let Pm and Cm,, respectively, denote the path and cycle on m vertices and K, denote the complete graph on n vertices. It is proved that （Km□Pm）=[n＋1/2]for m≥2,la（Km□Cm）=[n＋2/2],and la（Km□Km）=[n＋m-1/2]. The methods to decompose these graphs into linear forests are given in the proofs. Furthermore, the linear arboricity conjecture is true for these classes of graphs.展开更多
In the Forest Department of Bangladesh, a Participatory Agroforestry Program （PAP） was initiated at a denuded Sal forests area to protect the forest resources and to alleviate poverty amongst the local poor populati...In the Forest Department of Bangladesh, a Participatory Agroforestry Program （PAP） was initiated at a denuded Sal forests area to protect the forest resources and to alleviate poverty amongst the local poor population. We explored whether the PAP reduced poverty and what factors might be responsible for poverty alleviation. We used three poverty measurement methods： the Head Count Index, the Poverty Gap Index and the Foster-Greer-Thorbecke index to determine the extent poverty reduction. We used a linear regression model to determine the possible differences among factors in poverty reduction. Data were collected through semi structured questionnaires and face to face interviews within the study area. PAP proved effective at poverty alleviation, considerably improving the local situation. The linear regression model showed that PAP output explained the income differences in poverty reduction. Participants identified bureaucracy and illegal money demands by forest department officials, an uncontrolled market system, and underdeveloped road infrastructure as the main obstacles to reduction of poverty. Overall, PAP is quite successful in alleviating poverty. So this program might be of interest at other degraded forest areas as a tool to alleviate poverty.展开更多
The indexes of dependent variables of the measurement on the forest ecological benefits were defined according to the analysis of the multiple ecological benefits of forest. This indexes system includes waterreserving...The indexes of dependent variables of the measurement on the forest ecological benefits were defined according to the analysis of the multiple ecological benefits of forest. This indexes system includes waterreserving, soil and water conservation, wind and sand suppression, microclimate improvement, carbon dioxide assimilation, atmosphere purification, flood and drought mitigation, tourism resource and wild creature protection benefits. The main factors from the numerous factors that affect dependent variables were chosen as independent variables. At last, a multivariate linear model was established for measurement of forest ecological benefit. With this multivariate linear model the forest ecological benefit of China was calculated. The forest ecological benefit of China is 723816 million yuan per year, which equals to 23.07% of the gross domestic product of China.展开更多
Topographic attributes are often used as explanatory variables when providing spatial estimates of various environmental attribute response variables. Elevation of sampling locations can be derived from global positio...Topographic attributes are often used as explanatory variables when providing spatial estimates of various environmental attribute response variables. Elevation of sampling locations can be derived from global positioning systems (GPS) or digital elevation models (DEM). Given the potential for differences in elevation among these two data sources, especially in response to forest canopy cover, our objective was to compare GPS and DEM-derived elevation values during the dormant season. A non-parametric Wilcoxon test indicated GPS elevation was higher than DEM elevation with a mean difference of 6 m. Linear regression analysis indicated that GPS and DEM elevation were well correlated (R2 = 0.71, r = 0.84, p 【0.0001). Although elevation among the two data sources differed, the strong linear relationship allows for correction of elevation values in a predictable manner.展开更多
基金Supported by the National Natural Science Foundation of China(11071096,11171129)the Natural Science Foundation of Hubei Province(2016CFB146)Research Foundation of College of Economics,Northwest University of Political Science and Law(19XYKY07)
文摘For a fixed graph F,a graph G is F-saturated if it has no F as a subgraph,but does contain F after the addition of any new edge.The saturation number,sat(n,F),is the minimum number of edges of a graph in the set of all F-saturated graphs with order n.In this paper,we determine the saturation number sat(n,2P3∪tP2)and characterize the extremal graphs for n≥6t+8.
基金Acknowledgements The author would like to thank the anonymous referees for their valuable suggestions. This work was supported by the Natural Science Foundation of Fujian Province （No. 2011J01025）.
文摘The k-ary n-cube Qkn （n ≥2 and k ≥3） is one of the most popular interconnection networks. In this paper, we consider the problem of a fault- free Hamiltonian cycle passing through a prescribed linear forest （i.e., pairwise vertex-disjoint paths） in the 3-ary n-cube Qn^3 with faulty edges. The following result is obtained. Let E0 （≠θ） be a linear forest and F （≠θ） be a set of faulty edges in Q3 such that E0∩ F = 0 and ｜E0｜ ＋｜F｜ ≤ 2n - 2. Then all edges of E0 lie on a Hamiltonian cycle in Qn^3- F, and the upper bound 2n - 2 is sharp.
基金Supported by the Slovak VEGA (Grant No.1/4005/07)Spanish Research Council (Grant No.BFM2002-00412)
文摘A （p, q）-graph G is called super edge-magic if there exists a bijective function f ： V（G） U E（G） →{1, 2 p＋q} such that f（u）＋ f（v）＋f（uv） is a constant for each uv C E（G） and f（Y（G）） = {1,2,...,p}. In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees （mT）, all of them of the same order, grows at least exponentially with m.
基金supported by the National Natural Science Foundation of China(Nos.12125106,12271169,12331014)National Key R and D Program of China(No.2020YFA0713100)+1 种基金Anhui Initiative in Quantum Information Technologies(No.AHY150200)Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)。
文摘A linear forest is a graph consisting of paths.In this paper,the authors determine the maximum number of edges in an(m,n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n≥m when m is sufficiently large.
文摘Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by ex,(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated vertices.Let Ln,k be the family of all linear forests of n vertices with k edges.In this paper,Turan number of Berge-Ln,in an r-uniform hypergraph is studied.When r≥k+1 and 3≤r≤l[]=1,we determine 2 the exact value of ex,(n,Berge-Ln,)respectively.When K-1≤r≤k,we 2 determine the upper bound of ex,(n,Berge-Ln,).
文摘It is a well known fact that the linear arboricity of a k-regular graph is [(k+1)/2] fork=3,4. In this paper, we prove that if the number Of edges of a k-regular circulant is divisibleby [(k+1)/2], then its edge set can be partitioned into [(k+1)/2] isomorphic linear forests, fork=3,4.
基金The National Natural Science Foundation of China(No.10971025)
文摘A linear forest is a forest whose components are paths. The linear arboricity la （G） of a graph G is the minimum number of linear forests which partition the edge set E（G） of G. The Cartesian product G□H of two graphs G and H is defined as the graph with vertex set V（G□H） = {（u, v）｜ u ∈V（G）, v∈V（H） } and edge set E（G□H） = { （ u, x） （ v, Y）｜u=v and xy∈E（H）, or uv∈E（G） and x=y}. Let Pm and Cm,, respectively, denote the path and cycle on m vertices and K, denote the complete graph on n vertices. It is proved that （Km□Pm）=[n＋1/2]for m≥2,la（Km□Cm）=[n＋2/2],and la（Km□Km）=[n＋m-1/2]. The methods to decompose these graphs into linear forests are given in the proofs. Furthermore, the linear arboricity conjecture is true for these classes of graphs.
文摘In the Forest Department of Bangladesh, a Participatory Agroforestry Program （PAP） was initiated at a denuded Sal forests area to protect the forest resources and to alleviate poverty amongst the local poor population. We explored whether the PAP reduced poverty and what factors might be responsible for poverty alleviation. We used three poverty measurement methods： the Head Count Index, the Poverty Gap Index and the Foster-Greer-Thorbecke index to determine the extent poverty reduction. We used a linear regression model to determine the possible differences among factors in poverty reduction. Data were collected through semi structured questionnaires and face to face interviews within the study area. PAP proved effective at poverty alleviation, considerably improving the local situation. The linear regression model showed that PAP output explained the income differences in poverty reduction. Participants identified bureaucracy and illegal money demands by forest department officials, an uncontrolled market system, and underdeveloped road infrastructure as the main obstacles to reduction of poverty. Overall, PAP is quite successful in alleviating poverty. So this program might be of interest at other degraded forest areas as a tool to alleviate poverty.
文摘The indexes of dependent variables of the measurement on the forest ecological benefits were defined according to the analysis of the multiple ecological benefits of forest. This indexes system includes waterreserving, soil and water conservation, wind and sand suppression, microclimate improvement, carbon dioxide assimilation, atmosphere purification, flood and drought mitigation, tourism resource and wild creature protection benefits. The main factors from the numerous factors that affect dependent variables were chosen as independent variables. At last, a multivariate linear model was established for measurement of forest ecological benefit. With this multivariate linear model the forest ecological benefit of China was calculated. The forest ecological benefit of China is 723816 million yuan per year, which equals to 23.07% of the gross domestic product of China.
文摘Topographic attributes are often used as explanatory variables when providing spatial estimates of various environmental attribute response variables. Elevation of sampling locations can be derived from global positioning systems (GPS) or digital elevation models (DEM). Given the potential for differences in elevation among these two data sources, especially in response to forest canopy cover, our objective was to compare GPS and DEM-derived elevation values during the dormant season. A non-parametric Wilcoxon test indicated GPS elevation was higher than DEM elevation with a mean difference of 6 m. Linear regression analysis indicated that GPS and DEM elevation were well correlated (R2 = 0.71, r = 0.84, p 【0.0001). Although elevation among the two data sources differed, the strong linear relationship allows for correction of elevation values in a predictable manner.
