Stability for large forbidden subgraphs
نویسنده
چکیده
We strengthen the stability theorem of Erdős and Simonovits. Write Kr (s1, . . . , sr) for the complete r-partite graph with parts of size s1, . . . , sr and Tr (n) for the r-partite Turán graph of order n. Our main result is: For all r ≥ 2 and sufficiently small c > 0, ε > 0, for every graph G of order n with ⌈ (1− 1/r − ε)n2/2 ⌉ edges, one of the following conditions holds: (a) Kr+1 ( ⌊c lnn⌋ , . . . , ⌊c lnn⌋ , ⌈ n1− √ c ⌉) ⊂ G; (b) G differs from Tr (n) in fewer than ( ε1/3 + c1/(3r+3) ) n2 edges.
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عنوان ژورنال:
- Journal of Graph Theory
دوره 62 شماره
صفحات -
تاریخ انتشار 2009