A note on simplicial cliques
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Date
2021-09
Authors
Chudnovsky, Maria
Scott, Alex
Seymour, Paul
Spirkl, Sophie
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
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.
Description
The 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/
Keywords
induced subgraphs, claw-free, even-hole-free, simplicial clique