Author:
Castrillón Iván D.,Cruz Roberto,Reyes Enrique
Abstract
Let $G=(V,E)$ be a graph. If $G$ is a König graph or if $G$ is a graph without 3-cycles and 5-cycles, we prove that the following conditions are equivalent: $\Delta_{G}$ is pure shellable, $R/I_{\Delta}$ is Cohen-Macaulay, $G$ is unmixed vertex decomposable graph and $G$ is well-covered with a perfect matching of König type $e_{1},\dots,e_{g}$ without 4-cycles with two $e_i$'s. Furthermore, we study vertex decomposable and shellable (non-pure) properties in graphs without 3-cycles and 5-cycles. Finally, we give some properties and relations between critical, extendable and shedding vertices.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
7 articles.
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