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
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
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
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
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
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,).
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.
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.
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.
