Weighted well-covered graphs without image, image, image, image Original Research Article

A graph is well-covered if every maximal independent set has the same cardinality. The recognition problem of well-covered graphs is known to be co-NP-complete. Let image be a linear set function defined on the vertices of image. Then image is image-well-covered if all maximal independent sets of image are of the same weight. The set of weight functions image for which a graph is image-well-covered is a vector space. We prove that finding the vector space of weight functions under which an input graph is image-well-covered can be done in polynomial time, if the input graph contains neither image nor image nor image nor image.