Regularity, matchings and Cameron-Walker graphs

2018/09/14 by Trung, Tran Nam
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.05377

Abstract

Let G be a simple graph and let ν(G) be the matching number of G. It is well-known that \reg I(G) \leqslant ν(G)+1. In this paper we show that \reg I(G) = ν(G)+1 if and only if every connected component of G is either a pentagon or a Cameron-Walker graph.

Related

• Regularity of symbolic powers of edge ideals of Cameron-Walker graphs
• The v-number and Castelnuovo-Mumford regularity of graphs
• Matchings in regular graphs: minimizing the partition function
• Algebraic study on Cameron-Walker graphs
• The regularity of edge rings and matching numbers