2-factors in claw-free graphs (Q2725180)

The authors consider the question of the range of the number of cycles possible in a 2-factor of a 2-connected claw-free graph with sufficiently high minimum degree. In particular they show that for such a graph \(G\) of order \(n\geq 51\) with \(\delta(G)\geq \frac{n-2}{3}\), \(G\) contains a 2-factor with exactly \(k\) cycles, for \(1\leq k \leq \frac{n-24}{3}\). They also show that this result is sharp in the sense that if \(\delta(G)\) is lowered one cannot obtain the full range of values for \(k\).