On 2-factors in claw-free graphs Original Research Article

A graph is said claw-free if it contains no induced subgraph isomorphic to K1,3. We prove that if G is a claw-free graph with minimum degree δ⩾4, then G contains a 2-factor with at most 6n/(δ+2)−1 components. Moreover, together with a theorem of Choudoum and Paulraj (J. Graph Theory 15 (1991) 259–265) and one of Anstee (J. Algorithms 6 (1985) 112–131), it is polynomial (in O(n3)) to construct such a 2-factor.