For integers i, j, k with i ≥ j ≥ k 0, let Ni,j,kbe the graph obtained by identifying end vertices of three disjoint paths of lengths i, j, k to the vertices of a triangle. In this paper, we show that every 3-connected {K 1,3, N i, 7-i, 2}-free graph is hamiltonian, where i ∈ {4,5}. This result is sharp in the sense that no one of the numbers i, 7-i and 2 in N i, 7-i, 2can be repla...
