Matching numbers and the regularity of the Rees algebra of an edge ideal

2019/05/06 by Herzog, Jürgen, Hibi, Takayuki
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.02141

Abstract

The regularity of the Rees ring of the edge ideal of a finite simple graph is studied. We show that the matching number is a lower and matching number~+1 is an upper bound of the regularity, if the Rees algebra is normal. In general the induced matching number is a lower bound for the regularity, which can be shown by applying the squarefree divisor complex.

Related

• Regularity of normal Rees algebras of edge ideals of graphs
• The regularity of edge rings and matching numbers
• Dominating induced matchings of finite graphs and regularity of edge ideals
• Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs
• An upper bound for the regularity of powers of edge ideals