## October 2019

### Alexandr V. Kostochka, On Ramsey-type problems for paths and cycles in dense graphs

Room 1501, Bldg. E6-1, KAIST

A well-known Ramsey-type puzzle for children is to prove that among any 6 people either there are 3 who know each other or there are 3 who do not know each other. More generally, a graph $G$ arrows a graph $H$ if for any coloring of the edges of $G$ with two colors, there is a

## May 2021

### Hong Liu, Sublinear expander and embeddings sparse graphs

Zoom

A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory, including e.g. the odd cycle problem of Erdős and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some

## May 2022

### Gil Kalai, The Cascade Conjecture and other Helly-type Problems

Zoom ID: 868 7549 9085

For a set $X$ of points $x(1)$, $x(2)$, $\ldots$, $x(n)$ in some real vector space $V$ we denote by $T(X,r)$ the set of points in $X$ that belong to the convex hulls of r pairwise disjoint subsets of $X$. We let $t(X,r)=1+\dim(T(X,r))$. Radon's theorem asserts that If $t(X,1)< |X|$, then $t(X, 2) >0$. The first

## June 2022

### O-joung Kwon (권오정), Graph minor theory and beyond

Room 1501, Bldg. E6-1, KAIST

One of the important work in graph theory is the graph minor theory developed by Robertson and Seymour in 1980-2010. This provides a complete description of the class of graphs that do not contain a fixed graph H as a minor. Later on, several generalizations of H-minor free graphs, which are sparse, have been defined

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IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
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