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The toughness of a noncomplete graph $G$ is the maximum real number $t$ suchthat the ratio of $|S|$ to the number of components of $G-S$ is at least $t$for every cutset $S$ of $G$, and the toughness of a complete graph is definedto be $\infty$. Determining the toughness for a given graph is NP-hard.Chv\'{a}tal's toughness conjecture, stating that there exists a constant $t_0$such that every graph with toughness at least $t_0$ is hamiltonian, is stillopen for general graphs. A graph is called $(P_3\cup 2P_1)$-free if it does notcontain any induced subgraph isomorphic to $P_3\cup 2P_1$, the disjoint unionof $P_3$ and two isolated vertices. In this paper, we confirm Chv\'{a}tal'stoughness conjecture for $(P_3\cup 2P_1)$-free graphs by showing that every7-tough $(P_3\cup 2P_1)$-free graph on at least three vertices is hamiltonian.

Hamiltonian cycles in 7-tough $(P_3\cup 2P_1)$-free graphs