Two Forbidden Subgraph Pairs for Hamiltonicity of 3-Connected Graphs

Abstract

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.