Forest embeddings in regular graphs of large girth
β Scribed by D.G Kirkpatrick; D.G Corneil
- Book ID
- 107884139
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 767 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## Abstract Let __B(G)__ be the edge set of a bipartite subgraph of a graph __G__ with the maximum number of edges. Let __b~k~__ = inf{|__B(G)__|/|__E(G)__β__G__ is a cubic graph with girth at least __k__}. We will prove that lim~k β β~ __b~k~__ β₯ 6/7.
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