On Related Edges in Well-Covered Graphs without Cycles of Length 4 and 6

摘要

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.