On a conjecture of Thomassen concerning subgraphs of large girth

In 1983 C. Thomassen conjectured that for every k, g∈ℕ there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g. Kühn and Osthus [2004] proved the case g = 6. We give another proof for the case g = 6 which is based on a...

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Bibliographic Details
Published in:Journal of graph theory 2011-08, Vol.67 (4), p.316-331
Main Authors: Dellamonica Jr, Domingos, Koubek, Václav, Martin, Daniel M., Rödl, Vojtěch
Format: Article
Language:English
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Summary:In 1983 C. Thomassen conjectured that for every k, g∈ℕ there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g. Kühn and Osthus [2004] proved the case g = 6. We give another proof for the case g = 6 which is based on a result of Füredi [1983] about hypergraphs. We also show that the analogous conjecture for directed graphs is true. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:316‐331,2011
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.20534