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

  • Authors:

  • Zdeněk Ryjáček;Akira Saito;R. H. Schelp

  • Affiliations:

  • Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic;Department of Mathematics, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156-8550, Japan;Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 1999

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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