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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 Kf(d)? Mader asked this question in 1967 and f(d)=Θ(d) was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of Kd,d. However, this …

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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 independent domination of graphs with bounded maximum degree. Let G be a graph with maximum degree at most k where k≥1. We prove that …

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David Munhá Correia, Rainbow matchings

Zoom ID: 869 4632 6610 (ibsdimag)

I will discuss various results for rainbow matching problems. In particular, I will introduce a ‘sampling trick’ which can be used to obtain short proofs of old results as well as to solve asymptotically some well known conjectures. This is joint work with Alexey Pokrovskiy and Benny Sudakov.

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, and (iii) certain random variable on the boundary of a ball has a small tail. As applications, we show that the volume of intersection of …

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Seunghun Lee (이승훈), Transversals and colorings of simplicial spheres

Room B232 IBS (기초과학연구원)

Motivated from the surrounding property of a point set in Rd introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum transversal ratio of simplicial d-spheres, we provide two infinite constructions. The first construction gives infinitely …

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Andreas Holmsen, Some recent results on geometric transversals

Room B232 IBS (기초과학연구원)

A geometric transversal to a family of convex sets in Rd is an affine flat that intersects the members of the family. While there exists a far-reaching theory concerning 0-dimensional transversals (intersection patterns of convex sets), much less is known when it comes to higher-dimensional transversals. In this talk, I will present some new …

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Ron Aharoni, A strong version of the Caccetta-Haggkvist conjecture

Zoom ID: 869 4632 6610 (ibsdimag)

The Caccetta-Haggkvist conjecture, one of the best known in graph theory, is that in a digraph with n vertices in which all outdegrees are at least n/k there is a directed cycle of length at most k. This is known for  large values of k, relatively to n, and asymptotically for n large. A few …

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

Room B232 IBS (기초과학연구원)

For given k graphs G1,…,Gk over a common vertex set of size n, what conditions on Gi ensures a 'colorful' copy of H, i.e. a copy of H containing at most one edge from each Gi? Keevash, Saks, Sudakov, and Verstraëte defined exk(n,H) to be the maximum total number of edges of the graphs …

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Ken-ichi Kawarabayashi (河原林 健一), Toward Directed Graph Minor Theory

Zoom ID: 869 4632 6610 (ibsdimag)

Graph Minor project by Robertson and Seymour is perhaps the deepest theory in Graph Theory. It gives a deep structural characterization of graphs without any graph H as a minor. It also gives many exciting algorithmic consequences. In this work, I would like to talk about our attempt to extend Graph minor project to directed …

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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 one of u and v is coloured red. Bonnet, Kim, Thomassé, and Watrigant defined the twin-width of a graph G to be the minimum integer …

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IBS 이산수학그룹 Discrete Mathematics Group
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
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