A proof for a conjecture on the regularity of binomial edge ideals

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:180

Article

Malayeri, Mohammad Rouzbahani¹  Madani, Sara Saeedi^1,2  Kiani, Dariush^1,2 

[1] Amirkabir Univ Technol, Tehran Polytech, Dept Math & Comp Sci, Tehran, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

关键词: Binomial edge ideals;    Castelnuovo-Mumford regularity;    Compatible maps;    Clique disjoint edge sets;   

DOI  :  10.1016/j.jcta.2021.105432

来源: Elsevier

【 摘 要 】

In this paper we introduce the concept of clique disjoint edge sets in graphs. Then, for a graph G, we define the invariant eta(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 eta(G). This, in particular, settles a conjecture on the regularity of binomial edge ideals in full generality. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free