Matchings, coverings, and Castelnuovo-Mumford regularity

Details Matchings, coverings, and Castelnuovo-Mumford regularity Matchings, coverings, and Castelnuovo-Mumford regularity

2010-09-14

arxiv.org/abs/1009.2756v2

Mathematics

Combinatorics

9 pages; v2 improves exposition

Scientific paper

We show how co-chordal covers of the edges of a graph give upper bounds on the Castelnuovo-Mumford regularity of its edge ideal. The proof is by an easy application of a deep result of Kalai and Meshulam. We also give a topological proof of (slight improvements to) a lower bound observed by Katzman. Using results from the graph theory literature, we will be able to calculate and/or bound the Castelnuovo-Mumford regularity for edge ideals of several new classes of graphs.

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