Songling Shan
Published 2017-06-27Version 1
A graph is called $2K_2$-free if it does not contain two independent edges as an induced subgraph. Broersma, Patel, and Pyatkin showed that every 25-tough $2K_2$-free graph with at least three vertices is hamiltonian. In this paper, we improve the required toughness in this result from 25 to 3.
Toughness, 2-factors and Hamiltonian cycles in $2K_2$-free graphs
Hamiltonian cycles in tough $(P_2\cup P_3)$-free graphs
Spanning trees with at most 4 leaves in $K_{1,5}-$free graphs
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