Abstract
AbstractWe describe the simplicial complex $$\Delta $$
Δ
such that the initial ideal of the binomial edge ideal $$J_\textrm{G}$$
J
G
of G is the Stanley-Reisner ideal of $$\Delta $$
Δ
. By using $$\Delta $$
Δ
we show that if $$J_\textrm{G}$$
J
G
is $$(S_2)$$
(
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.
Funder
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory
Cited by
2 articles.
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