Matchings, coverings, and Castelnuovo-Mumford regularity

Abstract

We show that the co-chordal cover number of a graph G gives an upper bound for the Castelnuovo-Mumford regularity of the associated edge ideal. Several known combinatorial upper bounds of regularity for edge ideals are then easy consequences of covering results from graph theory, and we derive new upper bounds by looking at additional covering results.

12 pages; v4 has minor changes for publication

Cited by in corpus (7)

• Results on the regularity of square-free monomial ideals
• Linearity defect of edge ideals and Fröberg's theorem
• Regularity and $a$-invariant of Cameron--Walker graphs
• Betti numbers of monomial ideals via facet covers
• The regularity of some families of circulant graphs
• The size of Betti tables of edge ideals arising from bipartite graphs
• Algebraic properties of Levi graphs associated with curve arrangements