## “School of Mathematics”

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Paper   IPM / M / 16305
School of Mathematics
Title:   Regularity of binomial edge ideals of chordal graphs
Author(s):
 1 Sara Saeedi Madani 2 Dariush Kiani (Joint with M. Rouzbahani Malayeri)
Status:   Published
Journal: Collect. Math.
Year:  2020
Pages:   DOI: 10.1007/s13348-020-00293-3
Supported by:  IPM
Abstract:
In this paper we prove the conjectured upper bound for CastelnuovoâMumford regularity of binomial edge ideals posed in [23], in the case of chordal graphs. Indeed, we show that the regularity of any chordal graph G is bounded above by the number of maximal cliques of G, denoted by c(G). Moreover, we classify all chordal graphs G for which L(G) = c(G), where L(G) is the sum of the lengths of longest induced paths of connected components of G. We call such graphs strong interval graphs. We show that the regularity of a strong interval graph G coincides with L(G) as well as c(G).