Shedding vertices of vertex decomposable graphs Academic Article uri icon

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abstract

  • We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite families of well-covered graphs, none of which have this property. We use these results to provide a minimal counterexample to a conjecture of Villarreal regarding Cohen-Macaulay graphs.

authors

  • Van Tuyl, Adam
  • Baker, Jonathan
  • Meulen, Kevin N Vander
  • Tuyl, Adam Van