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Closure, 2‐factors, and cycle coverings in claw‐free graphs
Author(s) -
Ryjáček Zdeněk,
Saito Akira,
Schelp R. H.
Publication year - 1999
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199910)32:2<109::aid-jgt1>3.0.co;2-o
Subject(s) - combinatorics , mathematics , claw , closure (psychology) , graph , discrete mathematics , mechanical engineering , economics , engineering , market economy
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