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Regular graphs of large girth and arbitrary degree

✍ Scribed by Dahan, Xavier

Book ID: 124152449
Publisher: Springer-Verlag
Year: 2014
Tongue: English
Weight: 483 KB
Volume: 34
Category: Article
ISSN: 0209-9683
DOI: 10.1007/s00493-014-2897-6

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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)__‖__G__ is a cubic graph with girth at least __k__}. We will prove that lim~k → ∞~ __b~k~__ ≥ 6/7.