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 k-skeleton of the simplex is extendably shellable, for any k. We show that the stronger conjecture has a negative answer, by exhibiting an infinite family of counterexamples.
Non-ridge-chordal complexes whose clique complex has shellable Alexander dual / Benedetti, Bruno; Bolognini, Davide. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - ELETTRONICO. - 180:(2021). [10.1016/j.jcta.2021.105430]
Non-ridge-chordal complexes whose clique complex has shellable Alexander dual
Bolognini, Davide
2021-01-01
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 k-skeleton of the simplex is extendably shellable, for any k. We show that the stronger conjecture has a negative answer, by exhibiting an infinite family of counterexamples.| File | Dimensione | Formato | |
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