Certain classes of Cohen–Macaulay multipartite 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.

Keywords:

• Posets
• multipartite graphs
• Cohen–Macaulay graphs
• linear resolutions

2010 Mathematics Subject Classification:

• 05E40
• 13C14
• 13D02

Disclosure statement

No potential conflict of interest was reported by the authors.