  A graph $G$ is $H$-free if it has no induced subgraph isomorphic to $H$,
where $H$ is a graph. In this paper, we show that every $\frac{3}{2}$-tough
$(P_4 \cup P_{10})$-free graph has a 2-factor. The toughness condition of this
result is sharp. Moreover, for any $\varepsilon>0$ there exists a
$(2-\varepsilon)$-tough $2P_5$-free graph without a 2-factor. This implies that
the graph $P_4 \cup P_{10}$ is best possible for a forbidden subgraph in a
sense.
