기초과학연구원 이산수학그룹
We give a summary on the work of the last months related to Frankl's Union-Closed conjecture and its offsprings. The initial conjecture is stated as a theorem in extremal set …
In 1977, Erdős and Hajnal made the conjecture that, for every graph $H$, there exists $c>0$ such that every $H$-free graph $G$ has a clique or stable set of size …
Extremal Combinatorics studies the maximum or minimum size of finite objects (numbers, sets, graphs) satisfying certain properties. In this talk, I introduce the conjectures I solved on Extremal Combinatorics, and …
In 1993, Erdős, Hajnal, Simonovits, Sós and Szemerédi proposed to determine the value of Ramsey-Turán density $\rho(3,q)$ for $q\ge3$. Erdős et al. (1993) and Kim, Kim and Liu (2019) proposed …
In this talk, we will discuss the problem of determining the maximum number of edges in an n-vertex k-critical graph. A graph is considered k-critical if its chromatic number is …
Configurations of axis-parallel boxes in $\mathbb{R}^d$ are extensively studied in combinatorial geometry. Despite their perceived simplicity, there are many problems involving their structure that are not well understood. I will …
We consider the spanning tree embedding problem in dense graphs without bipartite holes and sparse graphs. In 2005, Alon, Krivelevich and Sudakov asked for determining the best possible spectral gap …
Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular, that for …
In 2006, Tao established the Gaussian counterpart of the celebrated Green-Tao theorem on arithmetic progressions of primes. In this talk, I will explain the extension of Tao's theorem and the …
For a given graph $H$, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of …