Universal graphs omitting finitely many finite graphs

Universal graphs omitting finitely many finite graphs

If F is a family of graphs, then a graph is F-free, if it contains no induced subgraph isomorphic to an element of F. If F is a finite set of finite graphs, λ is an infinite cardinal, we let CF(F,λ) be the minimal number of F-free graphs of size λ such that each F-free graph of size λ embeds into so...

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Veröffentlicht in:Discrete mathematics 2019-12, Vol.342 (12), p.111596, Article 111596
Hauptverfasser: Komjáth, Péter, Shelah, Saharon
Format: Artikel
Sprache:eng
Schlagworte:
Infinite graphs
Universal graphs
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Zusammenfassung:If F is a family of graphs, then a graph is F-free, if it contains no induced subgraph isomorphic to an element of F. If F is a finite set of finite graphs, λ is an infinite cardinal, we let CF(F,λ) be the minimal number of F-free graphs of size λ such that each F-free graph of size λ embeds into some of them. We show that if 2
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.111596