### Dong Yeap Kang (강동엽), A proof of the Erdős-Faber-Lovász conjecture

Zoom ID: 934 3222 0374 (ibsdimag)

A hypergraph is linear if every pair of two distinct edges shares at most one vertex. A longstanding conjecture by Erdős, Faber, and Lovász in 1972, states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this talk, I will present the ideas to prove the conjecture for

### Ron Aharoni, Colorful KKM and multiple cakes division

Zoom ID: 934 3222 0374 (ibsdimag)

In the "cake partition" problem n players have each a list of preferred parts for any partition of the interval ("cake") into n sub-intervals. Woodall, Stromquist and Gale proved independently that under mild conditions on the list of preferences (like continuity) there is always a partition and assignment of parts to the players, in which every player gets

### Jie Ma (马杰), TBA

Zoom ID: 934 3222 0374 (ibsdimag)

### David Wood, Tree densities of sparse graph classes

Zoom ID: 934 3222 0374 (ibsdimag)

This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\mathcal{G}$ as $n\to \infty$? I will answer this question for a variety of sparse graph classes $\mathcal{G}$. In particular, we show that the answer is

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209