Shedding vertices of vertex decomposable graphs
  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. 
Jonathan Baker, Kevin N. Vander Meulen, and Adam Van Tuyl
math.CO math.AC