Non-ridge-chordal complexes whose clique complex has shellable Alexander dual
Combinatorics
2020-11-26 v4 Commutative Algebra
Abstract
A recent conjecture that appeared in three papers by Bigdeli--Faridi, Dochtermann, and Nikseresht, is that every simplicial complex whose clique complex has shellable Alexander dual, is ridge-chordal. This strengthens the long-standing Simon's conjecture that the -skeleton of the simplex is extendably shellable, for any . We show that the stronger conjecture has a negative answer, by exhibiting an infinite family of counterexamples.
Cite
@article{arxiv.1910.06755,
title = {Non-ridge-chordal complexes whose clique complex has shellable Alexander dual},
author = {Bruno Benedetti and Davide Bolognini},
journal= {arXiv preprint arXiv:1910.06755},
year = {2020}
}
Comments
Substantial improvements. To appear on Journal of Combinatorial Theory, Series A