Abstract
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.
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