Dominating induced matchings of finite graphs and regularity of edge ideals

Abstract

The regularity of an edge ideal of a finite simple graph $G$ is at least the induced matching number of $G$ and is at most the minimum matching number of $G$. If $G$ possesses a dominating inuduced matching, i.e., an induced matching which forms a maximal matching, then the induced matching number of $G$ is equal to the minimum matching number of $G$. In the present paper, from viewpoints of both combinatorics and commutative algebra, finite simple graphs with dominating induced matchings will be mainly studied.

23 pages, v2:minor changes, to appear in Journal of Algebraic Combinatorics

References in corpus (3)

• Exact algorithms for dominating induced matchings
• Bounding Castelnuovo-Mumford regularity of graphs via Lozin's transformation
• Spectral results for the dominating induced matching problem