本文所说的图是简单图,未定义的术语见[1,2].n 阶图 G,n≥3,若有长为 n 的圈,则说 G 是汉米尔顿图;若对每个 k,3≤k≤n,G 含有长为 k 的圈,则说 G 是泛圈图.定理1.在 n 阶图 G 中,若对任何点对 x,y∈V(G),xy(?)E(G),都有 d(x)+d(y)≥n,...本文所说的图是简单图,未定义的术语见[1,2].n 阶图 G,n≥3,若有长为 n 的圈,则说 G 是汉米尔顿图;若对每个 k,3≤k≤n,G 含有长为 k 的圈,则说 G 是泛圈图.定理1.在 n 阶图 G 中,若对任何点对 x,y∈V(G),xy(?)E(G),都有 d(x)+d(y)≥n,则 G 是汉米尔顿图.展开更多
In this letter, we only consider simple graphs. Suppose that G is a graph with n vertices. If G contains a cycle of length n, then we say that G is Hamiltonian. If G contains a cycle of length k for each k, 3 ≤k≤n, ...In this letter, we only consider simple graphs. Suppose that G is a graph with n vertices. If G contains a cycle of length n, then we say that G is Hamiltonian. If G contains a cycle of length k for each k, 3 ≤k≤n, then G is pancyclic. We say that G is a vertex-k-cycle graph if G contains a cycle展开更多
Let G be a connected graph, SV(G) and u∈V(G). Write N(S)={v∈V(G)\S: there exists a vertex w∈S such that vw∈E(G)}, N(u)={v∈V(G):uv∈E(G)}, which are respectively called the neighborhood of S and u. Let (u)=N(u)∪{...Let G be a connected graph, SV(G) and u∈V(G). Write N(S)={v∈V(G)\S: there exists a vertex w∈S such that vw∈E(G)}, N(u)={v∈V(G):uv∈E(G)}, which are respectively called the neighborhood of S and u. Let (u)=N(u)∪{u} be the closed neighborhood of u, and G(u)= G|(u)| be the induced subgraph by N(u) in G. It is clear that |V(G(u))|=d_G(u)+1. A connected graph G is called an local Ore-type graph if and only if for any u∈ V(G), G(u) is a graph satisfying Ore’s condition, i. e.展开更多
In this letter, all graphs will be simple. The terminologies and notations, which we do not define, are standard. 1. A graph is called K1,3-free graph if the graph does not contain the induced subgraph isomorphic to K...In this letter, all graphs will be simple. The terminologies and notations, which we do not define, are standard. 1. A graph is called K1,3-free graph if the graph does not contain the induced subgraph isomorphic to K1,3. Recently, on characterizing Hamiltonian graphs by forbidden subgraphs,the K1,3-free graph is studied in many ways. A great many interesting results have been obtained. In this letter, we prove the展开更多
Ⅰ. BACKGROUND AND NOTATIONS In this paper all graphs will be finite, undirected, and have no loops or multiple edges, namely, simple graphs. E. Gyovi put the following question: Is there a (the smallest) natural numb...Ⅰ. BACKGROUND AND NOTATIONS In this paper all graphs will be finite, undirected, and have no loops or multiple edges, namely, simple graphs. E. Gyovi put the following question: Is there a (the smallest) natural number f(s,t) such that the vertex set of each graph of connectivity being f (s, t) at least has a decomposition into sets which would induce subgraphs of connectivity being展开更多
In this letter, all graphs will be finite, undirected, and have no loops or multiple edges. V(G) and E(G) denote respectively the vertex set and the edge set of the graph G. If S(?)V(G), then we denote by G[S] the sub...In this letter, all graphs will be finite, undirected, and have no loops or multiple edges. V(G) and E(G) denote respectively the vertex set and the edge set of the graph G. If S(?)V(G), then we denote by G[S] the subgraph induced by S in G. For the vertex u∈V(G), the neighborhood N(u) of u is the set of all vertices of G adjacent to u.展开更多
The concept of line graphs is familiar; the notation L(G) denotes the line graph of simile graph G. What conditions do the graph satisfy such that the line graph of G is Hamiltonian? Further, do these conditions imply...The concept of line graphs is familiar; the notation L(G) denotes the line graph of simile graph G. What conditions do the graph satisfy such that the line graph of G is Hamiltonian? Further, do these conditions imply that the L (G) is pancyclic? These problems are interesting.展开更多
In this letter, all graphs will be simple; most of the graph terminologies used here can be found in standard texts except those we don’t define. We know that if G is a graph of order n, and d(x)+d(y)≥n whenever xy(...In this letter, all graphs will be simple; most of the graph terminologies used here can be found in standard texts except those we don’t define. We know that if G is a graph of order n, and d(x)+d(y)≥n whenever xy(?) E(G), x, y∈V(G), then G is a Hamiltonian (Ore. 1960). Further, G is either展开更多
文摘本文所说的图是简单图,未定义的术语见[1,2].n 阶图 G,n≥3,若有长为 n 的圈,则说 G 是汉米尔顿图;若对每个 k,3≤k≤n,G 含有长为 k 的圈,则说 G 是泛圈图.定理1.在 n 阶图 G 中,若对任何点对 x,y∈V(G),xy(?)E(G),都有 d(x)+d(y)≥n,则 G 是汉米尔顿图.
文摘In this letter, we only consider simple graphs. Suppose that G is a graph with n vertices. If G contains a cycle of length n, then we say that G is Hamiltonian. If G contains a cycle of length k for each k, 3 ≤k≤n, then G is pancyclic. We say that G is a vertex-k-cycle graph if G contains a cycle
文摘Let G be a connected graph, SV(G) and u∈V(G). Write N(S)={v∈V(G)\S: there exists a vertex w∈S such that vw∈E(G)}, N(u)={v∈V(G):uv∈E(G)}, which are respectively called the neighborhood of S and u. Let (u)=N(u)∪{u} be the closed neighborhood of u, and G(u)= G|(u)| be the induced subgraph by N(u) in G. It is clear that |V(G(u))|=d_G(u)+1. A connected graph G is called an local Ore-type graph if and only if for any u∈ V(G), G(u) is a graph satisfying Ore’s condition, i. e.
文摘In this letter, all graphs will be simple. The terminologies and notations, which we do not define, are standard. 1. A graph is called K1,3-free graph if the graph does not contain the induced subgraph isomorphic to K1,3. Recently, on characterizing Hamiltonian graphs by forbidden subgraphs,the K1,3-free graph is studied in many ways. A great many interesting results have been obtained. In this letter, we prove the
文摘Ⅰ. BACKGROUND AND NOTATIONS In this paper all graphs will be finite, undirected, and have no loops or multiple edges, namely, simple graphs. E. Gyovi put the following question: Is there a (the smallest) natural number f(s,t) such that the vertex set of each graph of connectivity being f (s, t) at least has a decomposition into sets which would induce subgraphs of connectivity being
文摘In this letter, all graphs will be finite, undirected, and have no loops or multiple edges. V(G) and E(G) denote respectively the vertex set and the edge set of the graph G. If S(?)V(G), then we denote by G[S] the subgraph induced by S in G. For the vertex u∈V(G), the neighborhood N(u) of u is the set of all vertices of G adjacent to u.
文摘The concept of line graphs is familiar; the notation L(G) denotes the line graph of simile graph G. What conditions do the graph satisfy such that the line graph of G is Hamiltonian? Further, do these conditions imply that the L (G) is pancyclic? These problems are interesting.
文摘In this letter, all graphs will be simple; most of the graph terminologies used here can be found in standard texts except those we don’t define. We know that if G is a graph of order n, and d(x)+d(y)≥n whenever xy(?) E(G), x, y∈V(G), then G is a Hamiltonian (Ore. 1960). Further, G is either
