Abstract:A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space, denoted W CW (G).Let B be a complete bipartite induced subgraph of G on vertex sets of bipartition B X and B Y . Then B is generating if there exists an independent set S such that S ∪ … Show more
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