Matchings, coverings, and Castelnuovo-Mumford regularity
Copyright policy )Matchings, coverings, and Castelnuovo-Mumford regularity
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
- Mississippi Valley State University United States
- Washington University in St. Louis United States
regularity, 13F55, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, 05C70, covering of graphs, Combinatorial aspects of simplicial complexes, edge ideal, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 05E45, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05E45, 13F55, 05C70
regularity, 13F55, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, 05C70, covering of graphs, Combinatorial aspects of simplicial complexes, edge ideal, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 05E45, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05E45, 13F55, 05C70
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