Ramsey–Turán problems with small independence numbers

József Balogh, Ce Chen, Grace McCourt, Cassie Murley

Research output: Contribution to journalArticlepeer-review


Given a graph H and a function f(n), the Ramsey–Turán number RT(n,H,f(n)) is the maximum number of edges in an n-vertex H-free graph with independence number at most f(n). For H being a small clique, many results about RT(n,H,f(n)) are known and we focus our attention on H=Ks for s≤13. By applying Szemerédi's Regularity Lemma, the dependent random choice method and some weighted Turán-type results, we prove that these cliques have the so-called phase transitions when f(n) is around the inverse function of the off-diagonal Ramsey number of Kr versus a large clique Kn for some r≤s.

Original languageEnglish (US)
Article number103872
JournalEuropean Journal of Combinatorics
StatePublished - May 2024

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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