### Kevin Hendrey, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups

Room B232 IBS (기초과학연구원)

Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles.  However, in 1999, Reed proved an analogue for odd cycles by relaxing packing

### Debsoumya Chakraborti, Some classical problems in graph saturation

Room B232 IBS (기초과학연구원)

Graph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph $G$ is called $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$, but the addition of any edge creates a copy of $F$. The function $\operatorname{sat}(n,F)$ is defined to be the minimum number of edges in an $n$-vertex

### Casey Tompkins, TBA

Room B232 IBS (기초과학연구원)

### Yixin Cao (操宜新), Recognizing (unit) interval graphs by zigzag graph searches

Room B232 IBS (기초과학연구원)

Corneil, Olariu, and Stewart presented a recognition algorithm for interval graphs by six graph searches. Li and Wu simplified it to only four. The great simplicity of the latter algorithm is however eclipsed by the complicated and long proofs. The main purpose of this paper is to present a new and significantly shorter proof for

### Édouard Bonnet, Twin-width and ordered binary structures

Zoom ID: 934 3222 0374 (ibsdimag)

The twin-width of a graph G can be defined as the least integer d such that there is a sequence of length |V(G)| of (strictly) coarser and coarser partitions of its vertex set V(G), and every part X of every partition P of the sequence has at most d other parts Y of P with

### Sophie Spirkl, TBA

Zoom ID: 934 3222 0374 (ibsdimag)
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