Weighted Well-Covered Graphs without Cycles of Length 4, 5, 6 and 7
Discrete Mathematics
2010-09-17 v4 Computational Complexity
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.
Keywords
Cite
@article{arxiv.0901.0858,
title = {Weighted Well-Covered Graphs without Cycles of Length 4, 5, 6 and 7},
author = {Vadim E. Levit and David Tankus},
journal= {arXiv preprint arXiv:0901.0858},
year = {2010}
}
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10 pages