Closure, 2‐factors, and cycle coverings in claw‐free graphs

Abstract

In this article, we study cycle coverings and 2-factors of a claw-free graph and those of its closure, which has been defined by the first author (On a closure concept in claw-free graphs, J Combin Theory Ser B 70 (1997), 217–224). For a claw-free graph G and its closure cl(G), we prove: (1) V(G) is covered by k cycles in G if and only if V(cl(G)) is covered by k cycles of cl(G); and (2) G has a 2-factor with at most k components if and only if cl(G) has a 2-factor with at most k components. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 109–117, 1999