Balanced bipartite distance of $K_4$-free graphs

Fuente: arXiv
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Autores principales: Balogh, József, Buczek, Ignacy, Grzesik, Andrzej, Kuc, Piotr
Formato: Preprint
Publicado: 2026
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author Balogh, József
Buczek, Ignacy
Grzesik, Andrzej
Kuc, Piotr
author_facet Balogh, József
Buczek, Ignacy
Grzesik, Andrzej
Kuc, Piotr
contents We show that every $K_4$-free graph on $n$ vertices can be made balanced bipartite by removing at most $\frac{n^2}{9}$ edges. This proves a conjecture of Balogh, Clemen, and Lidický, and generalizes both Sudakov's result on the bipartite distance of $K_4$-free graphs and Reiher's result on the sparse half of $K_4$-free graphs.
format Preprint
id arxiv_https___arxiv_org_abs_2605_05346
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Balanced bipartite distance of $K_4$-free graphs
Balogh, József
Buczek, Ignacy
Grzesik, Andrzej
Kuc, Piotr
Combinatorics
We show that every $K_4$-free graph on $n$ vertices can be made balanced bipartite by removing at most $\frac{n^2}{9}$ edges. This proves a conjecture of Balogh, Clemen, and Lidický, and generalizes both Sudakov's result on the bipartite distance of $K_4$-free graphs and Reiher's result on the sparse half of $K_4$-free graphs.
title Balanced bipartite distance of $K_4$-free graphs
topic Combinatorics
url https://arxiv.org/abs/2605.05346