For integers i , j , k with $${i\geq j\geq k\geq 0}$$ , let N i , j , k be 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 $${i \in \{4,5\}}$$ . This result is sharp in the sense that no one of the numbers i , 7 i and 2 in N i , 7- i , 2 can be replaced by a larger number. For integers i , j , k with $${i\geq j\geq k\geq 0}$$ , let N i , j , k be the graph obtained by identifying end vertices of three disjoint paths o...
