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

Bruno Benedetti, Davide Bolognini

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Article number105430
JournalJournal of Combinatorial Theory. Series A
StatePublished - May 2021


  • Chordality
  • Simon's conjecture
  • Simplicial complexes
  • k-decomposability

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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