Making $K_{r+1}$-Free Graphs $r$-partite
Combinatorics
2022-05-03 v1
Abstract
The Erd\H{o}s-Simonovits stability theorem states that for all \epsilon >0 there exists \alpha >0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - \alpha n^2, then one can remove \epsilon n^2 edges from G to obtain an r-partite graph. F\"uredi gave a short proof that one can choose \alpha=\epsilon. We give a bound for the relationship of \alpha and \varepsilon which is asymptotically sharp as \epsilon \to 0.
Keywords
Cite
@article{arxiv.1910.00028,
title = {Making $K_{r+1}$-Free Graphs $r$-partite},
author = {József Balogh and Felix Christian Clemen and Mikhail Lavrov and Bernard Lidický and Florian Pfender},
journal= {arXiv preprint arXiv:1910.00028},
year = {2022}
}
Comments
12 pages, 1 figure