Maximum density of induced 5-cycle is achieved by an iterated blow-up of 5-cycle
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2016-02-01
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Lidicky, Bernard
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Mathematics
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Mathematics
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)=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, for n 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.
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This is a manuscript of an article published as Balogh, József, Ping Hu, Bernard Lidický, and Florian Pfender. "Maximum density of induced 5-cycle is achieved by an iterated blow-up of 5-cycle." European Journal of Combinatorics 52, Part A (2016): 47-58. doi: 10.1016/j.ejc.2015.08.006. Posted with permission.
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Thu Jan 01 00:00:00 UTC 2015