## “School of Mathematics”

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Paper   IPM / M / 16534
School of Mathematics
Title:   A proof for a conjecture on the regularity of binomial edge ideals
Author(s):
 1 Sara Saeedi Madani 2 Dariush Kiani (Joint with M. Rouzbahani Malayeri)
Status:   Published
Journal: J. Combin. Theory Ser. A
Vol.:  180
Year:  2021
Pages:   105432
Supported by:  IPM
Abstract:
In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a graph G, we define the invariant η(G) as the maximum size of a clique disjoint edge set in G. We show that the regularity of the binomial edge ideal of G is bounded above by η(G). This, in particular, settles a conjecture on the regularity of binomial edge ideals in full generality.