On the number of pentagons in triangle-free graphs
نویسندگان
چکیده
Using the formalism of flag algebras, we prove that the maximal number of copies of C5 in a triangle-free graph with 5l + a vertices (0 ≤ a ≤ 4) is l(l + 1)a, and we show that the set of extremal graphs for this problem consists precisely of almost balanced blow-ups of a single pentagon. This settles a conjecture made by Erdős in 1984. For the transition from an asymptotic version of our result to the exact one, we introduce a new technique based on replacing finite objects by their infinite blow-ups which we expect to have further applications.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 120 شماره
صفحات -
تاریخ انتشار 2013