For non-negative integers i,j and k,let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i,j and k to the vertices of a triangle.In this paper,we prove that every 3-connecte...For non-negative integers i,j and k,let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i,j and k to the vertices of a triangle.In this paper,we prove that every 3-connected {K1,3,N3,3,3 }-free graph is Hamiltonian.This result is sharp in the sense that for any integer i>3,there exist infinitely many 3-connected {K1,3,Ni,3,3 }-free non-Hamiltonian graphs.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.11071096 and 11271149)Hubei Provincial Department of Education (Grant No. D20111110)Jinan Science and Technology Bureau (Grant No. 20110205)
文摘For non-negative integers i,j and k,let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i,j and k to the vertices of a triangle.In this paper,we prove that every 3-connected {K1,3,N3,3,3 }-free graph is Hamiltonian.This result is sharp in the sense that for any integer i>3,there exist infinitely many 3-connected {K1,3,Ni,3,3 }-free non-Hamiltonian graphs.
