Binomial Edge Ideals of Complements of Graphs of Girth at Least 5

Abstract

We calculate the local cohomology modules of the binomial edge ideals of the complements of graphs of girth at least 5 using the tools introduced by Àlvarez Montaner in arXiv:1901.08645. We then use this calculation to compute the depth, dimension, and regularity of these binomial edge ideals.

18 pages, v4 removes the connectivity condition imposed in v1-v3, so many sections are reorganised and extended (although the techniques used are largely the same); v3 corrects typos; v2 includes small changes to several proofs for clarity, and reorganises section 2 into subsections (whilst some numbering has changed, no new results are introduced)