Abstract
A graph is calledwell-covered if all maximal independent subsets in it have the same number of elements. LetI be an independent subset (possibly empty) in a graphG. The subgraph ofG obtained by erasing the setI together with its neighborhood is calledcostable. We present a characterization of the class of well-covered graphs in terms of the minimal set of prohibited costable subgraphs. This characterization implies characterizations of some well-known subclasses of the class of well-covered graphs as well as the existence of a polynomial algorithm for the recognition of well-covered graphs with bounded valences.
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