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

Let C(n) denote the maximum number of induced copies of C5 in graphs on n vertices. For n large enough, we show that C(n) = a · b · c · d · e + 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, if n is 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.

• Type: Journal
• Year: 2016
• Where: EJC
• Authors: József Balogh, Ping Hu, Bernard Lidický, Florian Pfender
• Keywords: EJC 2016, Information Technology