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, no set can be added to $\mathcal F$ while preserving this property. In 1974, Erdős and Kleitman asked for the smallest possible size of a

Martin Milanič, Tree Decompositions with Bounded Independence Number

Zoom ID: 869 4632 6610 (ibsdimag)

The independence number of a tree decomposition $\mathcal{T}$ of a graph is the smallest integer $k$ such that each bag of $\mathcal{T}$ induces a subgraph with independence number at most $k$. If a graph $G$ is given together with a tree decomposition with bounded independence number, then the Maximum Weight Independent Set (MWIS) problem can

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 of which is 3-connected admits an essentially unique locally flat embedding into the 3-sphere, if it admits one at all. This can be thought of

Sebastian Wiederrecht, Matching Minors in Bipartite Graphs

Zoom ID: 869 4632 6610 (ibsdimag)

Matching minors are a specialisation of minors which preserves the existence and elementary structural properties of perfect matchings. They were first discovered as part of the study of the Pfaffian recognition problem on bipartite graphs (Polya's Permanent Problem) and acted as a major inspiration for the definition of butterfly minors in digraphs. In this talk

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 $Q_{m}$ or a red induced copy of $Q_{n}$. Axenovich and Walzer showed that $n+2\le R(Q_{2},Q_{n})\le2n+2$. Recently, Lu and Thompson improved the upper bound to $\frac{5}{3}n+2$. In

Tuukka Korhonen, Fast FPT-Approximation of Branchwidth

Zoom ID: 869 4632 6610 (ibsdimag)

Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically symmetric and submodular) functions could be decomposed into a tree-like structure by specific cuts. We develop a general framework for designing fixed-parameter tractable (FPT) 2-approximation algorithms for branchwidth of connectivity functions. The first ingredient of our framework is combinatorial. We prove a structural theorem establishing

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 $f(d) = \Theta(\sqrt{d})$ was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of $K_{d,d}$. However, this

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 $k \ge 1$. We prove that

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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