摘要
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.
For non-negative integers i,j and k, let Ni,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.
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)
