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arXiv · 2007.09959

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

M. Rouzbahani Malayeri·S. Saeedi Madani·D. Kiani
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Abstract

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.

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M. Rouzbahani Malayeri, S. Saeedi Madani, D. Kiani. 2020-07-20. A proof for a conjecture on the regularity of binomial edge ideals. https://arxiv.org/abs/2007.09959

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