기초과학연구원 이산수학그룹
Fix $r \ge 2$ and consider a family F of $C_{2r+1}$-free graphs, each having minimum degree linear in its number of vertices. Such a family is known to have bounded …
Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate …
The first course in graph theory usually covers concepts such as matchings, independent sets, colourings, and forbidden subgraphs. Around 2004, Borgs, Chayes, Lovász, Sós, Szegedy, and Vestergombi introduced a very …
We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches …
A circle graph is an intersection graph of a set of chords of a circle. In this talk, I will describe the unavoidable induced subgraphs of circle graphs with large …
Let $G=\mathbb{F}_p^n$. Which systems of linear equations $\Psi$ have the property that amongst all subsets of $G$ of fixed density, random subsets minimise the number of solutions to $\Psi$? This …
A subset $A\subseteq \mathbb Z$ of integers is free if for every two distinct subsets $B, B'\subseteq A$ we have \Pisier asked if for every subset $A\subseteq \mathbb Z$ of …
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 …
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 …
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 …