A lower bound on the independence number of a graph
نویسندگان
چکیده
منابع مشابه
A lower bound on the independence number of a graph
For a connected and non-complete graph, a new lower bound on its independence number is proved. It is shown that this bound is realizable by the well known efficient algorithm MIN.
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The independence number of a graph G, denoted α(G), is the maximum cardinality of an independent set of vertices in G. The independence number is one of the most fundamental and well-studied graph parameters. In this paper, we strengthen a result of Fajtlowicz [Combinatorica 4 (1984), 35–38] on the independence of a graph given its maximum degree and maximum clique size. As a consequence of our...
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For a given connected graph G on n vertices and m edges, we prove that its independence number α(G) is at least ((2m+n+2)-((2m+n+2) 2-16n 2) ½)/8. Intoduction Let G=(V,E) be a connected graph G on n=│V│ vertices and m=│E│ edges. For a subgraph H of G and for a vertex i∈V(H), let d H (i) be the degree of i in H and let N H (i) be its neighbourhood in H. Let δ(H) and ∆(H) be the minimum degree an...
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We propose a new lower bound on the independence number of a graph. We show that our bound compares favorably to recent ones (e.g. [12]). We obtain our bound by using the Bhatia-Davis inequality applied with analytical results (minimum, maximum, expectation and variance) of an algorithm for the vertex cover problem.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00048-x