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Paper   IPM / M / 15367
School of Mathematics
  Title:   Binomial edge ideals of regularity 3
1.  Sara Saeedi Madani
2.  Dariush Kiani
  Status:   Published
  Journal: J. Algebra
  Vol.:  515
  Year:  2018
  Pages:   157-172
  Supported by:  IPM
et J_G be the binomial edge ideal of a graph G. We characterize all graphs whose binomial edge ideals, as well as their initial ideals, have regularity 3. Consequently we characterize all graphs G such that J_G is extremal Gorenstein. Indeed, these characterizations are consequences of an explicit formula we obtain for the regularity of the binomial edge ideal of the join product of two graphs. Finally, by using our regularity formula, we discuss some open problems in the literature. In particular we disprove a conjecture in [5] on the regularity of weakly closed graphs.

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