combinatorics / Extremal graph theory
Zhu, Gyori, He, Lv, Salia and Xiao conjectured the maximum number of copies of a fixed cycle in an $n$-vertex graph of bounded circumference, attained by the join of a clique with an independent set. For every fixed $s \ge 3$ and $L \ge 2s+2$ and all large $n$, $\mathrm{ex}(n, C_{2s+1}, \mathcal{C}_{\ge L+1}) = N(C_{2s+1}, H(n,L))$. Together with the companion even-cycle result this settles the conjecture.
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Append-only history
the odd-cycle half; the even-cycle half is a companion paper by the same authors
Research memory
Zhu, Gyori, He, Lv, Salia and Xiao conjectured the maximum number of copies of a fixed cycle in an $n$-vertex graph of bounded circumference, attained by the join of a clique with an independent set. For every fixed $s \ge 3$ and $L \ge 2s+2$ and all large $n$, $\mathrm{ex}(n, C_{2s+1}, \mathcal{C}_{\ge L+1}) = N(C_{2s+1}, H(n,L))$. Together with the companion even-cycle result this settles the conjecture.
the odd-cycle half; the even-cycle half is a companion paper by the same authors
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