On the bipartite density of regular graphs with large girth
Ondřej Zýka · Journal of Graph Theory · 1990
Abstract Let B(G) be the edge set of a bipartite subgraph of a graph G with the maximum number of edges. Let bk = inf{|B(G)|/|E(G)‖G is a cubic graph with girth at least k}. We will prove that limk → ∞ bk ≥ 6/7.