On well-covered, vertex decomposable and Cohen-Macaulay graphs

Iván Dario Castrillón, Roberto Cruz, Enrique Reyes

Let $G=(V,E)$ be a graph. If $G$ is a König graph or $G$ is a graph without 3-cycles and 5-cycle, we prove that the following conditions are equivalent: ${\Delta }_G$ is pure shellable,…