Abstract
Let k≥2 be an integer. We say that a graph G is (K2∪kK1)-free if it does not contain K2∪kK1 as an induced subgraph. Recently, Shi and Shan conjectured that every 1-tough and 2k-connected (K2∪kK1)-free graph is hamiltonian. In this paper, we solve this conjecture by proving that every 1-tough and k-connected (K2∪kK1)-free graph with minimum degree at least 3(k−1)2 is hamiltonian or the Petersen graph.
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