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A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G):H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NP-hard problem to determine the bipartite density of any given triangle-free cubic graph. Bondy and Locke gave a polynomial time algorithm which, given a triangle-free subcubic...
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