TY - JOUR
T1 - Ramsey–Turán problems with small independence numbers
AU - Balogh, József
AU - Chen, Ce
AU - McCourt, Grace
AU - Murley, Cassie
N1 - Publisher Copyright:
© 2023
PY - 2024/5
Y1 - 2024/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.ejc.2023.103872
DO - 10.1016/j.ejc.2023.103872
M3 - Article
AN - SCOPUS:85177747812
SN - 0195-6698
VL - 118
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103872
ER -