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Non-ridge-chordal complexes whose clique complex has shellable Alexander dual

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arxiv 1910.06755 v4 pith:BZR7R5YG submitted 2019-10-15 math.CO math.AC

Bruno Benedetti , Davide Bolognini This is my paper · ORCID
classification math.COmath.AC
keywords complexconjectureshellablealexandercliquedualwhoseanswer
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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.

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  1. Extendable shellability for $d$-dimensional complexes on $d+3$ vertices

    math.CO 2019-08 conditional novelty 6.0 of 10

    Every shellable d-dimensional simplicial complex with at most d+3 vertices is extendably shellable, proved through exposed-edge deletions in chordal graphs.

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