Binomial edge ideals of bipartite complements of even cycles

Shahnawaz Ahmad Rather; S. Pirzada; M. Aijaz

paper

Binomial edge ideals of bipartite complements of even cycles

arXiv:2609.32860

Abstract

Let $G_{n}$ be the bipartite complement of the even cycle $C_{2 n}$ , and let $J_{G_{n}}$ be its binomial edge ideal. For $n \geq 5$ , we study the interaction between the combinatorial structure of $G_{n}$ and the algebraic invariants of $S_{G_{n}} / J_{G_{n}}$ . Our main combinatorial ingredient is a classification of the subsets of $V (G_{n})$ having the cut point property, obtained through an analysis of disconnected induced subgraphs of $G_{n}$ . We use this classification to describe the minimal primes and to study dimension and degree-theoretic invariants of $J_{G_{n}}$ and $S_{G_{n}} / J_{G_{n}}$ . We also study local Vasconcelos numbers, graded Betti numbers and the Hilbert series, and obtain information on projective dimension and depth. Finally, we analyze induced paths in $G_{n}$ and derive corresponding bounds for the Castelnuovo--Mumford regularity.