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Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie
Discrete mathematics, September 2021, 2021-09-00, Volume: 344, Issue: 9Journal Article
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.
