Abstract
AbstractA graph is called a ‐free graph if it does not contain as an induced subgraph. In 2014, Broersma, Patel, and Pyatkin showed that every 25‐tough ‐free graph on at least three vertices is Hamiltonian. Recently, Shan improved this result by showing that 3‐tough is sufficient instead of 25‐tough. In this paper, we show that every 2‐tough ‐free graph on at least three vertices is Hamiltonian, which was conjectured by Gao and Pasechnik.
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