For non-negative integers i,j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that e...For non-negative integers i,j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that every 3-connected {K1,3,N8-i,i,1}-free graph is hamiltonian, where 1〈i〈4.展开更多
A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show t...A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show that if G is.3-connected claw-free graph and(1)if for each vertex V the set of venices at distance three from v doesn’tcontain and independent subset of size three,then G is hamiltonian;(2) if G contains no induced subgraph with degree sequence(1,1,1,2,2,2,3,3,3),so that ear vertel of degree is adjacent to a vertex of degree i + 1 for i=1,2,then G is hamiltonoan. Furthermore,we obtain a generalization of both(1) and(2),in which the graphs F1 and F2coatain an the known forbidded subgraphs given in[3] as indeced subgraphs.展开更多
基金Supported by the National Natural Science Foundation of China(No.11371162 and No.11271149)A project of Shandong Province Higher Educational Science and Technology Program(No.J15LI52)Science and Technology Development Project of Shandong Province(No.2014GGX101033)
文摘For non-negative integers i,j and k, we denote the generalized net as Ni,j,k, which is a triangle with disjoint paths of length i, j and k, attached to distinct vertices of the triangle. In this paper, we prove that every 3-connected {K1,3,N8-i,i,1}-free graph is hamiltonian, where 1〈i〈4.
文摘A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show that if G is.3-connected claw-free graph and(1)if for each vertex V the set of venices at distance three from v doesn’tcontain and independent subset of size three,then G is hamiltonian;(2) if G contains no induced subgraph with degree sequence(1,1,1,2,2,2,3,3,3),so that ear vertel of degree is adjacent to a vertex of degree i + 1 for i=1,2,then G is hamiltonoan. Furthermore,we obtain a generalization of both(1) and(2),in which the graphs F1 and F2coatain an the known forbidded subgraphs given in[3] as indeced subgraphs.
基金supported by NSFSD(No.BS2010SF017,Y2008A04)NNSFC(No.11101245)+1 种基金Foundation of Education Committee of Shandong Province(J07YH03)Foundation of Shandong Institute of Business and Technology(2011QF073)
