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October 13, 2025Open Access

On the Ramsey-Tur\'an problem for 4-cliques

Key Points

A tight bound for the ramsey-turán problem for 4-cliques is established, enhancing previous limits.
The findings show significant extension in edge bounds for k4-free graphs based on the independence number.
The study avoids using the regularity lemma, offering a novel methodology for bounding edges.
New insights potentially benefit graph theory and combinatorial optimization fields.

Abstract

We present an essentially tight bound for the Ramsey-Tur\'an 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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Béla Csaba (Sat,) studied this question.

www.synapsesocial.com/papers/68ecc715d1cc7436f7d18b29 — DOI: https://doi.org/10.48550/arxiv.2503.00644

On the Ramsey-Tur\'an problem for 4-cliques

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