Certain Classes of Cohen-Macaulay Multipartite Graphs
Rajiv Kumar, Ajay Kumar
TL;DR
This paper investigates the Cohen-Macaulay property in graphs derived from specific relations on sets, identifying new classes of multipartite graphs with this property.
Contribution
It introduces a novel approach to determine Cohen-Macaulayness in graphs from reflexive and antisymmetric relations, expanding understanding of such graph classes.
Findings
Identifies classes of multipartite graphs that are Cohen-Macaulay
Provides criteria for Cohen-Macaulayness based on relations
Extends previous studies on Cohen-Macaulay properties in graphs
Abstract
The Cohen-Macaulay property of a graph arising from a poset has been studied by various authors. In this article, we study the Cohen-Macaulay property of a graph arising from a family of reflexive and antisymmetric relations on a set. We use this result to find classes of multipartite graphs which are Cohen-Macaulay.
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