Multidegrees of binomial edge ideals
Abstract
Let $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In particular, we study the set $S_{\min}(G)$ defined as the collection of subsets of vertices whose prime ideals have minimum codimension. We provide results which assist in determining $S_{\min}(G)$, then calculate $S_{\min}(G)$ for star, horned complete, barbell, cycle, wheel, and friendship graphs, and use the main result of the paper to obtain the multidegrees of their binomial edge ideals.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.07365
 arXiv:
 arXiv:2405.07365
 Bibcode:
 2024arXiv240507365C
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 13H15;
 05C25 (Primary) 05E40;
 14C17 (Secondary)
 EPrint:
 12 pages, 3 figures, submitted to the Proceedings of the AMS