Two Forbidden Subgraph Pairs for Hamiltonicity of 3-Connected Graphs.

For integers i, j, k with $${i\geq j\geq k\geq 0}$$, let N 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, N}-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 can be replaced by a larger number. [ABSTRACT FROM AUTHOR]