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Making $K_{r+1}$-Free Graphs $r$-partite

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 نشر من قبل Bernard Lidick\\'y
 تاريخ النشر 2019
  مجال البحث
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The ErdH{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. Furedi 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.



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