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-NPC. The complexity status of the problem is not known if the input is restricted to graphs with no cycles of length 4. We conjecture that the problem is polynomial if the input graph does not contain cycles of length 4 and 6, and prove several theorems supporting our conjecture.
|Title of host publication
|Graph Theory, Computational Intelligence and Thought - Essays Dedicated to Martin Charles Golumbic on the Occasion of His 60th Birthday
|Marina Lipshteyn, Vadim E. Levit, Ross M. McConnell
|Number of pages
|Published - 2009
|Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)