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Disjoint cycles in star-free graphs

✍ Scribed by Markus, Lisa R.; Snevily, Hunter S.

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 322 KB
Volume: 21
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199604)21:4<425::aid-jgt8>3.0.co;2-r

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✦ Synopsis

A graph is claw-free if it does not contain K l , 3 as an induced subgraph. It is Kl,,-free if it does not contain K l , r as an induced subgraph. We show that if a graph is Kl,,-free ( r 2 4), only p + 2r -1 edges are needed to insure that G has t w o disjoint cycles.

As an easy consequence w e get a well-known result of Posa's. 0 1996 John Wiley & Sons. Inc.

Let G be a K,,,-free graph (Y 2 4). If q 2 p + 2r -1 then G contains As a corollary we get the following well-known result of Posa.

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