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

✍ Scribed by Ryj�?ek, Zden?k; Saito, Akira; Schelp, R. H.

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
239 KB
Volume
32
Category
Article
ISSN
0364-9024

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✦ Synopsis

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

(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.

📜 SIMILAR VOLUMES

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In the class of k-connected claw-free graphs, we study the stability of some Hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these

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We study the cycle structure of I-tough, triangle-free graphs. In particular, w e prove that every such graph on n 2 3 vertices with minimum degree 6 2 i ( n + 2) has a 2-factor. W e also show this is best possible by exhibiting an infinite class of I-tough, triangle-free graphs having 6 = $ ( n + 1