设G是一个图。令 NC(G)=min{|N(u)∪N(V)|{u,v)(?)V(G),uv(?)E(G)},本文主要结论如下:定理1 设 G 是3—连通图,|V(G)|=n,{a,b)(?)V(G).若 G 含有一条(a,b)—控制路,则 G 中存在(a,b)—控制路 P,使得|V(P)|≥min{n,2NC(G)-1}定理2 设 G ...设G是一个图。令 NC(G)=min{|N(u)∪N(V)|{u,v)(?)V(G),uv(?)E(G)},本文主要结论如下:定理1 设 G 是3—连通图,|V(G)|=n,{a,b)(?)V(G).若 G 含有一条(a,b)—控制路,则 G 中存在(a,b)—控制路 P,使得|V(P)|≥min{n,2NC(G)-1}定理2 设 G 是3—连通图,|V(G)|=n,NC(G)≥1/2(n+1).若对于任意{a,b)(?)V(G),G 中都有(a.b)—控制路,则 G 是 Hamilton—连通的。展开更多
In this letter all graphs will be finite, undirected simple graphs. Let G be a graph. we shall use V（G） and E（G） to denote the vertex set and the edge set of G respectively, and let p=, |V（G）|. Let UV（G）. We s...In this letter all graphs will be finite, undirected simple graphs. Let G be a graph. we shall use V（G） and E（G） to denote the vertex set and the edge set of G respectively, and let p=, |V（G）|. Let UV（G）. We shall use G[U] to denote the subgraph induced by U. A graph G is K1, 3-free if G[U]K1, 3 for any UV（G）. A graph G is m-path-connected if there is a （u, v）-path of length at least m for any {u, v} V（G）.展开更多
In this letter we consider only undirected simple graphs. Let G he a graph, we shall use V(G) and E(G) to denote the vertex set and the edge set of G respectively. And let u,v∈V(G), we denote the degree of v by d(u) ...In this letter we consider only undirected simple graphs. Let G he a graph, we shall use V(G) and E(G) to denote the vertex set and the edge set of G respectively. And let u,v∈V(G), we denote the degree of v by d(u) and the edge joining u and v by uv.展开更多
Throughout this letter, all graphs will be finite, undirected, simple graphs. A K1,3-free graph is a graph with no induced subgraph isomorphic to K1,3. In 1980, B. Jackson proved that all 2-connected, k-regular graphs...Throughout this letter, all graphs will be finite, undirected, simple graphs. A K1,3-free graph is a graph with no induced subgraph isomorphic to K1,3. In 1980, B. Jackson proved that all 2-connected, k-regular graphs on at most 3k vertices are Hamiltonian. Further, in 1986, Y. J. Zhu, Z. H. Liu and Z. F. Yu展开更多
Let G be a 3-connected graph with n vertices, is an independent set of G} , MC(G)=min is an independent set in G}.In this paper, the main results are as follows.TheoremⅠ. If then G is Hamilton-connected.TheoremⅡ. If...Let G be a 3-connected graph with n vertices, is an independent set of G} , MC(G)=min is an independent set in G}.In this paper, the main results are as follows.TheoremⅠ. If then G is Hamilton-connected.TheoremⅡ. If, then G is Hamilton-connected.Theorems I and IIare the best possible, and are incomparable in the sense that neither theorem implies the other.展开更多
Let G be an undirected simple graph, t be a positive integer. Write; Y is an independent set of G, |Y|=t}. For Y∈I_t(G), i∈{0, 0, …, t}, set S_i(Y):={v∈V(G); |N(v)∩Y|=i}, s_i(Y):=|S_i(Y)|. In 1990, Chen Guan-tao ...Let G be an undirected simple graph, t be a positive integer. Write; Y is an independent set of G, |Y|=t}. For Y∈I_t(G), i∈{0, 0, …, t}, set S_i(Y):={v∈V(G); |N(v)∩Y|=i}, s_i(Y):=|S_i(Y)|. In 1990, Chen Guan-tao et al. introduced the following definition.展开更多
In this paper, we prove that a non-negative rational number sequence (a1,a2,... ,ak+1) is k-Hamilton-nice, if (1) and (2) implies for arbitrary i1,i2,...,i h∈{1,2,... ,k}. This result was conjectured by Guantao Chen ...In this paper, we prove that a non-negative rational number sequence (a1,a2,... ,ak+1) is k-Hamilton-nice, if (1) and (2) implies for arbitrary i1,i2,...,i h∈{1,2,... ,k}. This result was conjectured by Guantao Chen and R.H. Schelp, and it generalizes several well-known sufficient conditions for graphs to be Hamiltonian.展开更多
文摘设G是一个图。令 NC(G)=min{|N(u)∪N(V)|{u,v)(?)V(G),uv(?)E(G)},本文主要结论如下:定理1 设 G 是3—连通图,|V(G)|=n,{a,b)(?)V(G).若 G 含有一条(a,b)—控制路,则 G 中存在(a,b)—控制路 P,使得|V(P)|≥min{n,2NC(G)-1}定理2 设 G 是3—连通图,|V(G)|=n,NC(G)≥1/2(n+1).若对于任意{a,b)(?)V(G),G 中都有(a.b)—控制路,则 G 是 Hamilton—连通的。
文摘In this letter all graphs will be finite, undirected simple graphs. Let G be a graph. we shall use V（G） and E（G） to denote the vertex set and the edge set of G respectively, and let p=, |V（G）|. Let UV（G）. We shall use G[U] to denote the subgraph induced by U. A graph G is K1, 3-free if G[U]K1, 3 for any UV（G）. A graph G is m-path-connected if there is a （u, v）-path of length at least m for any {u, v} V（G）.
文摘In this letter we consider only undirected simple graphs. Let G he a graph, we shall use V(G) and E(G) to denote the vertex set and the edge set of G respectively. And let u,v∈V(G), we denote the degree of v by d(u) and the edge joining u and v by uv.
文摘Throughout this letter, all graphs will be finite, undirected, simple graphs. A K1,3-free graph is a graph with no induced subgraph isomorphic to K1,3. In 1980, B. Jackson proved that all 2-connected, k-regular graphs on at most 3k vertices are Hamiltonian. Further, in 1986, Y. J. Zhu, Z. H. Liu and Z. F. Yu
文摘Let G be a 3-connected graph with n vertices, is an independent set of G} , MC(G)=min is an independent set in G}.In this paper, the main results are as follows.TheoremⅠ. If then G is Hamilton-connected.TheoremⅡ. If, then G is Hamilton-connected.Theorems I and IIare the best possible, and are incomparable in the sense that neither theorem implies the other.
基金Project supported by the National Natural Science Foundation of China.
文摘Let G be an undirected simple graph, t be a positive integer. Write; Y is an independent set of G, |Y|=t}. For Y∈I_t(G), i∈{0, 0, …, t}, set S_i(Y):={v∈V(G); |N(v)∩Y|=i}, s_i(Y):=|S_i(Y)|. In 1990, Chen Guan-tao et al. introduced the following definition.
文摘In this paper, we prove that a non-negative rational number sequence (a1,a2,... ,ak+1) is k-Hamilton-nice, if (1) and (2) implies for arbitrary i1,i2,...,i h∈{1,2,... ,k}. This result was conjectured by Guantao Chen and R.H. Schelp, and it generalizes several well-known sufficient conditions for graphs to be Hamiltonian.
