%A Grzesik, Andrzej
%A Kielak, BartÅ‚omiej
%D 2019
%T On the maximum number of odd cycles in graphs without smaller odd cycles
%K
%X We prove that for each odd integer $k \geq 7$ , every graph on $n$ vertices without odd cycles of length less than $k$ contains at most $(n/k)^k$ cycles of length~ $k$ . This generalizes the previous results on the maximum number of pentagons in triangle-free graphs , conjectured by Erd \H os in 1984, and asymptotically determines the generalized Tur \'an number $\mathrm{ex}(n,C_k,C_{k-2})$ for odd $k$ . In contrast to the previous results on the pentagon case, our proof is not computer - assisted .
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1234
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 755-758%V 88
%N 3
%@ 0862-9544
%8 2019-07-30