(S2)-condition and Cohen–Macaulay binomial edge ideals

We describe the simplicial complex Δ such that the initial ideal of the binomial edge ideal J G of G is the Stanley-Reisner ideal of Δ . By using Δ we show that if J G is ( S 2 ) , then G is accessible. We also characterize all accessible blocks with whiskers of cycle rank 3 and we define a new infi...

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Published in	Journal of algebraic combinatorics Vol. 57; no. 2; pp. 589 - 615
Main Authors	Lerda, Alberto, Mascia, Carla, Rinaldo, Giancarlo, Romeo, Francesco
Format	Journal Article
Language	English
Published	New York Springer US 01.03.2023 Springer Nature B.V
Subjects	Accessibility Algebra Apexes Combinatorics Computer Science Convex and Discrete Geometry Decomposition Graph theory Graphs Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures 05E40 Serre’s condition Cohen–Macaulay rings 13C05 05C25 13C14 Binomial edge ideals Accessible chain of cycles
Online Access	Get full text
ISSN	0925-9899 1572-9192 1572-9192
DOI	10.1007/s10801-022-01173-8

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Summary:	We describe the simplicial complex Δ such that the initial ideal of the binomial edge ideal J G of G is the Stanley-Reisner ideal of Δ . By using Δ we show that if J G is ( S 2 ) , then G is accessible. We also characterize all accessible blocks with whiskers of cycle rank 3 and we define a new infinite class of accessible blocks with whiskers for any cycle rank. Finally, by using a computational approach, we show that the graphs with at most 12 vertices whose binomial edge ideal is Cohen–Macaulay are all and only the accessible ones.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0925-9899 1572-9192 1572-9192
DOI:	10.1007/s10801-022-01173-8