On line graphs of subcubic triangle-free graphs
نویسندگان
چکیده
منابع مشابه
Bipartite density of triangle-free subcubic graphs
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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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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We present some results on the structure of line graphs of triangle-free graphs and discuss connections with homogeneity.
متن کاملThe fractional chromatic number of triangle-free subcubic graphs
Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 ≈ 2.909.
متن کاملTriangle-free subcubic graphs with minimum bipartite density
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 su...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.01.006