Recognizing Generating Subgraphs Revisited

A graph [Formula: see text] is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function defined on vertices. Then text]well-covered weight. For every text], set functions such text]-well-covered vector space, denoted as WCW(G). Deciding whether an input co-NP-complete. Therefore, finding WCW(G) co-NP-hard. generating subgraph induced complete bipartite vertex bipartition and each for some text]. If generating, then subgraphs play important role in The decision problem known to be NP-complete. In this article we prove NP- completeness graphs without cycles length 3 5, with girth at least 6. On other hand, supply polynomial algorithms recognizing WCW(G), when We also present algorithm which finds does not contain lengths 3, 4, 7.