The Erds-Pósa Property for Long Circuits

For an integer at least 3, we prove that if G is a graph containing no two vertex-disjoint circuits of length at least , then there is a set X of at most 5 3 + 29 2 vertices that intersects all circuits of length at least . Our result improves the bound 2 + 3 due to Birmelé, Bondy, and Reed (The Erd...

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Bibliographic Details
Published inJournal of graph theory Vol. 77; no. 4; p. 251
Main Authors Meierling, Dirk, Rautenbach, Dieter, Sasse, Thomas
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.12.2014
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Summary:For an integer at least 3, we prove that if G is a graph containing no two vertex-disjoint circuits of length at least , then there is a set X of at most 5 3 + 29 2 vertices that intersects all circuits of length at least . Our result improves the bound 2 + 3 due to Birmelé, Bondy, and Reed (The Erds-Pósa property for long circuits, Combinatorica 27 (2007), 135-145) who conjecture that vertices always suffice.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21769