기초과학연구원 이산수학그룹
For a given hypergraph $H$ and a vertex $v\in V(H)$, consider a random matching $M$ chosen uniformly from the set of all matchings in $H.$ In $1995,$ Kahn conjectured that …
For a family F of graphs, the F-Deletion Problem asks to remove the minimum number of vertices from a given graph G to ensure that G belongs to F. One …
Depth and width parameters of graphs, e.g., tree-width, path-width and tree-depth, play a crucial role in algorithmic and structural graph theory. These notions are of fundamental importance in the theory …
For the past few years, I've been working on formalizing proofs in matroid theory using the Lean proof assistant. This has led me to many interesting and unexpected places. I'll …
Every (finite) matroid consists of a (finite) set called the ground set, and a collection of distinguished subsets called the independent sets. A classic example arises when the ground set …
In 1980, Burr conjectured that every directed graph with chromatic number $2k-2$ contains any oriented tree of order $k$ as a subdigraph. Burr showed that chromatic number $(k-1)^2$ suffices, which …
An edge-colored graph $H$ is called rainbow if all of its edges are given distinct colors. An edge-colored graph $G$ is then called rainbow $H$-free when no copy of $H$ in …
We prove the following variant of Helly’s classical theorem for Hamming balls with a bounded radius. For $n > t$ and any (finite or infinite) set $X$, if in a …
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 …
Rödl and Ruciński established Ramsey's theorem for random graphs. In particular, for fixed integers $r$, $\ell\geq 2$ they showed that $n^{-\frac{2}{\ell+1}}$ is a threshold for the Ramsey property that every …