Maximal independent sets in the covering graph of the cube

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Maximal independent sets in the covering graph of the cube

Several familiar problems in extremal set theory can be cast as questions about the maximum possible size of an independent set defined on a suitable graph, about the total number of independent sets in such graphs, or about enumeration of the maximal independent sets. Here we find bounds on the number of maximal independent sets in the covering graph of a hypercube. © 2010 Elsevier B.V. All ri...

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15 صفحه اول

On the number of maximal independent sets in a graph

Let G be a (simple, undirected, finite) graph. A set S ⊆ V (G) is independent if no edge of G has both its endpoints in S. An independent set S is maximal if no independent set of G properly contains S. Let MIS(G) be the set of all maximal independent sets in G. Miller and Muller (1960) and Moon and Moser (1965) independently proved that the maximum, taken over all n-vertex graphs G, of |MIS(G)...

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ژورنال

عنوان ژورنال: Discrete Applied Mathematics

سال: 2013

ISSN: 0166-218X

DOI: 10.1016/j.dam.2010.09.003