Weighted Well-Covered Graphs without Cycles of Length 4, 5, 6 and 7
(0901.0858)Abstract
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 w be a weight function defined on the vertices of G. Then G is w-well-covered if all maximal independent sets of G are of the same weight. The set of weight functions w for which a graph is w-well-covered is a vector space. We prove that finding the vector space of weight functions under which an input graph is w-well-covered can be done in polynomial time, if the input graph does not contain cycles of length 4, 5, 6 and 7.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.