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Making Kr+1-free graphs r-partite
Combinatorics, Probability and Computing ( IF 0.9 ) Pub Date : 2020-11-10 , DOI: 10.1017/s0963548320000590 József Balogh , Felix Christian Clemen , Mikhail Lavrov , Bernard Lidický , Florian Pfender
Combinatorics, Probability and Computing ( IF 0.9 ) Pub Date : 2020-11-10 , DOI: 10.1017/s0963548320000590 József Balogh , Felix Christian Clemen , Mikhail Lavrov , Bernard Lidický , Florian Pfender
The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a K r+ 1 -free graph on n vertices with e (G ) > ex(n , K r +1 )– α n 2 , then one can remove εn 2 edges from G to obtain an r -partite graph. Füredi gave a short proof that one can choose α = ε . We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.
中文翻译:
制作无 Kr+1 的图 r-partite
Erdős–Simonovits 稳定性定理指出,对于所有ε > 0 存在α > 0 使得如果G 是一个ķ r+ 1 - 免费图表n 顶点与e (G ) > 前(n ,ķ r +1 )–α n 2 ,然后可以删除εn 2 边缘从G 获得一个r - 分图。Füredi 给出了一个可以选择的简短证明α =ε . 我们给出了关系的界限α 和ε 这是渐近尖锐的ε → 0。
更新日期:2020-11-10
中文翻译:
制作无 Kr+1 的图 r-partite
Erdős–Simonovits 稳定性定理指出,对于所有