## January 2022

### Andreas Holmsen, Some recent results on geometric transversals

Room B232 IBS (기초과학연구원)

A geometric transversal to a family of convex sets in $\mathbb R^d$ is an affine flat that intersects the members of the family. While there exists a far-reaching theory concerning

### Jaehyeon Seo (서재현), A rainbow Turán problem for color-critical graphs

Room B232 IBS (기초과학연구원)

For given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensures a 'colorful' copy of $H$, i.e. a copy of $H$ containing

### O-joung Kwon (권오정), Reduced bandwidth: a qualitative strengthening of twin-width in minor-closed classes (and beyond)

Room B232 IBS (기초과학연구원)

In a reduction sequence of a graph, vertices are successively identified until the graph has one vertex. At each step, when identifying $u$ and $v$, each edge incident to exactly

## February 2022

### Pascal Gollin, A unified 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

### Jinha Kim (김진하), Independent domination of graphs with bounded maximum degree

Room B232 IBS (기초과학연구원)

An independent dominating set of a graph, also known as a maximal independent set, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is

### Donggyu Kim (김동규), A stronger version of Tutte’s wheel theorem for vertex-minors

Room B232 IBS (기초과학연구원)

Tutte (1961) proved that every simple $3$-connected graph $G$ has an edge $e$ such that $G \setminus e$ or $G / e$ is simple $3$-connected, unless $G$ is isomorphic to

### Sang-il Oum (엄상일), Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k

Room B232 IBS (기초과학연구원)

Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for

## March 2022

### Kevin Hendrey, A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups (revisited)

Room B232 IBS (기초과학연구원)

This talk follows on from the recent talk of Pascal Gollin in this seminar series, but will aim to be accessible for newcomers. Erdős and Pósa proved in 1965 that

### Tuan Anh Do, Rank- and tree-width of supercritical random graphs

Room B232 IBS (기초과학연구원)

It is known that the rank- and tree-width of the random graph $G(n,p)$ undergo a phase transition at $p = 1/n$; whilst for subcritical $p$, the rank- and tree-width are bounded above

### Jaehoon Kim (김재훈), Ramsey numbers of cycles versus general graphs

Room B232 IBS (기초과학연구원)

The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a

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