On the binomial edge ideals of proper interval graphs

2016/11/30 by Baskoroputro, Herolistra
#05C25 #05E40 #13C05 #13C14 #13C15 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.10117

Abstract

We prove several cases of the Betti number conjecture for the binomial edge ideal J_G of a proper interval graph G (also known as closed graph). Namely, we show that this conjecture is true for the linear strand of J_G, and true in general for any proper interval graph G such that the regularity of S/J_G equals two.

Related

• On the regularity of binomial edge ideals
• On the extremal Betti numbers of the binomial edge ideal of closed graphs
• On the Betti numbers of some classes of Binomial edge ideals
• Depth and Extremal Betti Number of Binomial Edge Ideals
• Extremal Betti numbers of some classes of binomial edge ideals