On October 11, 2022, Nika Salia from the IBS Extremal Combinatorics and Probability Group gave a talk at the Discrete Math Seminar on the maximum number of bicliques in a graph without an even cycle of a fixed length at the Discrete Math Seminar. The title of his talk was “Exact results for generalized extremal problems forbidding an even cycle“.

## Welcome Nika Salia and Zixiang Xu, new members of the IBS Extremal Combinatorics and Probability Group

The IBS discrete mathematics group welcomes Dr. Nika Salia and Dr. Zixiang Xu (徐子翔), new research fellows at the IBS Extremal Combinatorics and Probability Group from September 1, 2022.

Dr. Nika Salia received his Ph.D. from the Central European University in 2021 under the supervision of Prof. Ervin Győri.

Dr. Zixiang Xu (徐子翔) received his Ph.D. from the Capital Normal University of China in 2022 under the supervision of Prof. Gennian Ge.

## Nika Salia, Exact results for generalized extremal problems forbidding an even cycle

We determine the maximum number of copies of $K_{s,s}$ in a $C_{2s+2}$-free $n$-vertex graph for all integers $s \ge 2$ and sufficiently large $n$. Moreover, for $s\in\{2,3\}$ and any integer $n$ we obtain the maximum number of cycles of length $2s$ in an $n$-vertex $C_{2s+2}$-free bipartite graph.

This is joint work with Ervin Győri (Renyi Institute), Zhen He (Tsinghua University), Zequn Lv (Tsinghua University), Casey Tompkins (Renyi Institute), Kitti Varga (Technical University of Budapest BME), and Xiutao Zhu (Nanjing University).