## October 2021

### Eunjin Oh (오은진), Feedback Vertex Set on Geometric Intersection Graphs

Room B232 IBS (기초과학연구원)

I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time $2^{O(\sqrt{k})}(n + ### Joonkyung Lee (이준경), Majority dynamics on sparse random graphs Room B232 IBS (기초과학연구원) Majority dynamics on a graph$G$is a deterministic process such that every vertex updates its$\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. ### Donggyu Kim (김동규), 𝝘-graphic delta-matroids and their applications Room B232 IBS (기초과학연구원) Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define ## November 2021 ### Ben Lund, Maximal 3-wise intersecting families Room B232 IBS (기초과학연구원) A family$\mathcal F$of subsets of {1,2,…,n} is called maximal k-wise intersecting if every collection of at most k members from$\mathcal F$has a common element, and moreover, ### Jaehoon Kim (김재훈), 2-complexes with unique embeddings in 3-space Room B232 IBS (기초과학연구원) A well-known theorem of Whitney states that a 3-connected planar graph admits an essentially unique embedding into the 2-sphere. We prove a 3-dimensional analogue: a simply-connected 2-complex every link graph ### Casey Tompkins, Ramsey numbers of Boolean lattices Room B232 IBS (기초과학연구원) The poset Ramsey number$R(Q_{m},Q_{n})$is the smallest integer$N$such that any blue-red coloring of the elements of the Boolean lattice$Q_{N}$has a blue induced copy of$Q_{m}$### Seonghyuk Im (임성혁), Large clique subdivisions in graphs without small dense subgraphs Room B232 IBS (기초과학연구원) What is the largest number$f(d)$where every graph with average degree at least$d$contains a subdivision of$K_{f(d)}$? Mader asked this question in 1967 and$f(d) = \Theta(\sqrt{d})$## December 2021 ### Eun-Kyung Cho (조은경), Independent domination of graphs with bounded maximum degree Room B232 IBS (기초과학연구원) The independent domination number of a graph$G$, denoted$i(G)$, is the minimum size of an independent dominating set of$G$. In this talk, we prove a series of results regarding ### Tuan Tran, Exponential decay of intersection volume with applications on list-decodability and sphere-covering bounds Room B232 IBS (기초과학연구원) We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, ## January 2022 ### Seunghun Lee (이승훈), Transversals and colorings of simplicial spheres Room B232 IBS (기초과학연구원) Motivated from the surrounding property of a point set in$\mathbb{R}^d\$ introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simplicial sphere. As

기초과학연구원 수리및계산과학연구단 이산수학그룹
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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