### Yunbum Kook (국윤범), Vertex Sparsification for Edge Connectivity

Room B232 IBS (기초과학연구원)

Graph compression or sparsification is a basic information-theoretic and computational question. A major open problem in this research area is whether $(1+\epsilon)$-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. As a step towards this goal, we initiate the study of a thresholded version of the problem: for a given parameter $c$,

### Tuan Tran, Anti-concentration phenomena

Room B232 IBS (기초과학연구원)

Let $X$ be a real random variable; a typical anti-concentration inequality asserts that (under certain assumptions) if an interval $I$ has small length, then $\mathbb{P}(X\in I)$ is small, regardless the location of $I$. Inequalities of this type have found powerful applications in many branches of mathematics. In this talk we will discuss several recent applications

### Gwenaël Joret, Packing and covering balls in graphs excluding a minor

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In 2007, Chepoi, Estellon, and Vaxès conjectured that there exists a universal constant $c>0$ such that the following holds for every positive integers $r$ and $k$, and every planar graph $G$: Either $G$ contains $k$ vertex-disjoint balls of radius $r$, or there is a subset of vertices of size at most $c k$ meeting all

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### Sebastian Siebertz, Rank-width meets stability

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Forbidden graph characterizations provide a convenient way of specifying graph classes, which often exhibit a rich combinatorial and algorithmic theory. A prime example in graph theory are classes of bounded tree-width, which are characterized as those classes that exclude some planar graph as a minor. Similarly, in model theory, classes of structures are characterized by

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