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

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

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 part...

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Hauptverfasser: Malayeri, M. Rouzbahani, Madani, S. Saeedi, Kiani, D
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Commutative Algebra
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Zusammenfassung: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.
DOI:10.48550/arxiv.2007.09959