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- W2013425391 abstract "Using the formalism of flag algebras, we prove that every triangle-free graph $G$ with $n$ vertices contains at most $(n/5)^5$ cycles of length five. Moreover, the equality is attained only when $n$ is divisible by five and $G$ is the balanced blow-up of the pentagon. We also compute the maximal number of pentagons and characterize extremal graphs in the non-divisible case provided $n$ is sufficiently large. This settles a conjecture made by ErdH{o}s in 1984." @default.
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- W2013425391 date "2013-04-01" @default.
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- W2013425391 title "On the number of pentagons in triangle-free graphs" @default.
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- W2013425391 doi "https://doi.org/10.1016/j.jcta.2012.12.008" @default.
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