기초과학연구원 이산수학그룹
In 1980, Burr conjectured that every directed graph with chromatic number
An edge-colored graph
We prove the following variant of Helly’s classical theorem for Hamming balls with a bounded radius. For
We say that a 0-1 matrix A contains another such matrix (pattern) P if P can be obtained from a submatrix of A by possibly changing a few 1 entries to 0. The main question of this theory is to estimate the maximal number of 1 entries in an n by n 0-1 matrix NOT …
Rödl and Ruciński established Ramsey's theorem for random graphs. In particular, for fixed integers
In general, random walks on fractal graphs are expected to exhibit anomalous behaviors, for example heat kernel is significantly different from that in the case of lattices. Alexander and Orbach in 1982 conjectured that random walks on critical percolation, a prominent example of fractal graphs, exhibit mean field behavior; for instance, its spectral dimension is …
This talk will first introduce combinatorics on permutations and patterns, presenting the basic notions and some fundamental results: the Marcus-Tardos theorem which bounds the density of matrices avoiding a given pattern, and the Guillemot-Marx algorithm for pattern detection using the notion now known as twin-width. I will then present a decomposition result: permutations avoiding a …
A classical problem in combinatorial geometry, posed by Erdős in 1946, asks to determine the maximum number of unit segments in a set of
We will give an overview of the recent attempts of building a structure theory for graphs centered around First-Order transductions: a notion of containment inspired by finite model theory. Particularly, we will speak about the notions of monadic dependence and monadic stability, their combinatorial characterizations, and the developments on the algorithmic front.
The IBS-DIMAG Workshop on Topology and Combinatorics will be held on November 11, 2024 at Room B332, Institute for Basic Science (IBS), Daejeon, South Korea. Invited Speakers (tentative) Karim Adiprasito (Jussieu Institute of Mathematics) Minho Cho조민호 (IBS Extremal Combinatorics and Probability Group) Niloufar Fuladi (INRIA Center of Université de Lorraine) Minki Kim김민기 (GIST) Dohyeon Lee이도현 (KAIST & …