We prove that every graph of minimum degree at least r and girth at least 186 contains a subdivision of K rΓΎ1 and that for r5435 a girth of at least 15 suffices. This implies that the conjecture of Haj ! o os that every graph of chromatic number at least r contains a subdivision of K r (which is fal
β¦ LIBER β¦
Topological Subgraphs in Graphs of Large Girth
β Scribed by W. Mader
- Publisher
- Springer-Verlag
- Year
- 1998
- Tongue
- English
- Weight
- 182 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
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In 1983 C. Thomassen conjectured that for every k, g β 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. KΓΌhn and Osthus [2004] proved the case g = 6. We give another proof for the case g = 6 which is based