منابع مشابه
An upper bound for the number of independent sets in regular graphs
Write I(G) for the set of independent sets of a graph G and i(G) for |I(G)|. It has been conjectured (by Alon and Kahn) that for an N -vertex, d-regular graph G, i(G) ≤ ( 2 − 1 )N/2d . If true, this bound would be tight, being achieved by the disjoint union ofN/2d copies ofKd,d. Kahn established the bound for bipartite G, and later gave an argument that established i(G) ≤ 2 N 2 (1+ 2 d) for G n...
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It was conjectured by Reed [12] that for any graph G, the graph’s chromatic number χ(G) is bounded above by l ∆(G)+1+ω(G) 2 m , where ∆(G) and ω(G) are the maximum degree and clique number of G, respectively. In this paper we prove that this bound holds if G is the line graph of a multigraph. The proof yields a polynomial time algorithm that takes a line graph G and produces a colouring that ac...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.06.031