Bounds on the regularity of toric ideals of graphs

2016/05/23 by Jennifer Biermann, Biermann, Jennifer, Augustine O'Keefe +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1605.06980

17 pages

arxiv created 2016/05/23 · arxiv updated 2016/05/24

Abstract

Let G be a finite simple graph. We give a lower bound for the Castelnuovo-Mumford regularity of the toric ideal I_G associated to G in terms of the sizes and number of induced complete bipartite graphs in G. When G is a chordal bipartite graph, we find an upper bound for the regularity of I_G in terms of the size of the bipartition of G. We also give a new proof for the graded Betti numbers of the toric ideal associated to the complete bipartite graph K_2,n.

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