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An upper bound for the number of maximal independent sets in a graph
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V. E. Alekseev
Published/Copyright:
December 4, 2007
Abstract
Let T(G) be the number of maximal independent sets, M(G) be the number of generated matchings in a graph G. We prove the inequality T(G) ≤ M(G) + 1. As a corollary, we derive the bound
for a graph containing no generated subgraph (p + 1)K2, where m is the number of edges and m1 is the number of dominating edges. This inequality differs from the Balas–Yu conjecture only in the presence of the last term.
Published Online: 2007-12-04
Published in Print: 2007-10-19
© de Gruyter
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- A general approach to studying the stability of a Pareto optimal solution of a vector integer linear programming problem
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