Castelnuovo-Mumford Regularity of Graph Ideals

Abstract

Let \(G\) be a simple graph with edge ideal \(I(G)\). In this article, we study the number of pairwise \(3\)-disjoint edges of cycles and complements of triangle-free graphs. Using that, we determine the Castelnuovo-Mumford regularity of \(R/I(G)\) for the above classes of graphs according to the number of pairwise \(3\)-disjoint edges.