# Noon lecture

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On 03.09.2015 at 12:20 in S4, there is the following noon lecture:

# Maximum density of induced 5-cycle is achieved by an iterated blow-up of 5-cycle

## Ping Hu

## Abstract

Let C(n) denote the maximum number of induced copies of 5-cycles in graphs on n vertices. For n large enough, we show that C(n)=abcde + C(a)+C(b)+C(c)+C(d)+C(e), where a+b+c+d+e = n and a,b,c,d,e are as equal as possible. Moreover, for n being a power of 5, we show that the unique graph on n vertices maximizing the number of induced 5-cycles is an iterated blow-up of a 5-cycle. The proof uses flag algebra computations and stability methods.

Joint work with Balogh, Lidický and Pfender.

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