Chudnovsky, MariaScott, AlexSeymour, PaulSpirkl, Sophie2022-08-122022-08-122021-09https://doi.org/10.1016/j.disc.2021.112470http://hdl.handle.net/10012/18522The final publication is available at Elsevier via https://doi.org/10.1016/j.disc.2021.112470. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/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 ε 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.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/induced subgraphsclaw-freeeven-hole-freesimplicial cliqueArticle