On the Ramsey-Turán problem for 4-cliques

2025/03/01 by Béla Csaba, Csaba, Béla
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2503.00644

openalex publication_date 2025/03/01 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

We present an essentially tight bound for the Ramsey-Turán problem for 4-cliques without using the Regularity lemma. This enables us to substantially extend the range in which one has the tight bound for the number of edges in K₄-free graphs as a function of the independence number, apart from lower order terms.

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• Ramsey-Turán Problems with small independence numbers
• Generalized Ramsey--Turán density for cliques
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