In a previous paper we obtained an upper bound for the minimum number of components of a 2-factor in a claw-free graph. This bound is sharp in the sense that there exist infinitely many claw-free graphs for which the bound is tight. In this paper we extend these results by presenting a polynomial algorithm that constructs a 2-factor of a claw-free graph with minimum degree at least four whose number of components meets this bound. As a byproduct we show that the problem of obtaining a minimum 2-factor (if it exists) is polynomially solvable for a subclass of claw-free graphs. As another byproduct we give a short constructive proof for a result of Ryjáček, Saito and Schelp.udud
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机译：在先前的论文中，我们获得了无爪图中2因子的最小数量的上限。在存在无限多个无爪图的严格意义上，此边界是尖锐的。在本文中，我们通过提出一种多项式算法扩展了这些结果，该算法构造了一个无爪图的2因子，其最小次数至少为4，且其分量数满足此限制。作为副产品，我们表明对于无爪图的子类，获得最小2因子（如果存在）的问题在多项式上可以解决。作为另一个副产品，我们对Ryjáček，Saito和Schelp的结果给出了简短的建设性证明。 ud ud
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