Dense Induced Bipartite Subgraphs in Triangle-Free Graphs
نویسندگان
چکیده
منابع مشابه
Bipartite subgraphs of triangle-free subcubic graphs
Suppose G is a graph with n vertices and m edges. Let n′ be the maximum number of vertices in an induced bipartite subgraph of G and let m′ be the maximum number of edges in a spanning bipartite subgraph of G. Then b(G) = m′/m is called the bipartite density of G, and b∗(G) = n′/n is called the bipartite ratio of G. This paper proves that every 2connected triangle-free subcubic graph, apart fro...
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A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is defined as b(G) = max{|E(B)|/|E(G)| : B is a bipartite subgraph of G}. It was conjectured by Bondy and Locke that if G is a triangle-free subcubic graph, then b(G) ≥ 45 and equality holds only if G is in a list of seven small graphs. The conjecture has been confirmed recently by Xu and Yu. This note gi...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2020
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-019-4086-0