Abstract

AbstractA graph is ‐free if it has no induced subgraph isomorphic to , where is a graph. In this paper, we show that every ‐tough ‐free graph has a 2‐factor. The toughness condition of this result is sharp. Moreover, for any there exists a ‐tough ‐free graph without a 2‐factor. This implies that the graph is best possible for a forbidden subgraph in a sense.

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