A proof of the stability of extremal graphs, Simonovits' stability from Szemerédi's regularity
نویسنده
چکیده
The following sharpening of Turán’s theorem is proved. Let Tn,p denote the complete p– partite graph of order n having the maximum number of edges. If G is an n-vertex Kp+1-free graph with e(Tn,p) − t edges then there exists an (at most) p-chromatic subgraph H0 such that e(H0) ≥ e(G)− t. Using this result we present a concise, contemporary proof (i.e., one using Szemerédi’s regularity lemma) for the classical stability result of Simonovits [21].
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 115 شماره
صفحات -
تاریخ انتشار 2015