A note on simplicial cliques

Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl

Research output: Contribution to journalArticlepeer-review


Motivated by an application in condensed matter physics and quantum information theory, we prove that every non-null even-hole-free claw-free graph has a simplicial clique, that is, a clique K such that for every vertex v∈K, the set of neighbours of v outside of K is a clique. In fact, we prove the existence of a simplicial clique in a more general class of graphs defined by forbidden induced subgraphs.

Original languageEnglish (US)
Article number112470
JournalDiscrete Mathematics
Issue number9
StatePublished - Sep 2021

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


  • Claw-free
  • Even-hole-free
  • Induced subgraphs
  • Simplicial clique


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