기초과학연구원 이산수학그룹
For fixed integers $r\ge 3, e\ge 3$, and $v\ge r+1$, let $f_r(n,v,e)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph in which the union of arbitrary $e$ …
A linear $3$-graph is called a (3-)hypertree if there exists exactly one path between each pair of two distinct vertices. A linear $3$-graph is called a Steiner triple system if …
Finding the smallest integer $N=ES_d(n)$ such that in every configuration of $N$ points in $\mathbb{R}^d$ in general position, there exist $n$ points in convex position is one of the most …
The disjoint paths logic, FOL+DP, is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1,y_1,\ldots,x_k,y_k),$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i,$ …
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 …
Various types of independent sets have been studied for decades. As an example, the minimum number of maximal independent sets in a connected graph of given order is easy to …
The Graphic Travelling Salesman Problem is the problem of finding a spanning closed walk (a TSP walk) of minimum length in a given connected graph. The special case of the …
I will first introduce the notion of recognisability of languages of terms and then its extensions to sets of relational structures. In a second step, I will discuss relations with …
We introduce the notion of delineation. A graph class $\mathcal C$ is said delineated by twin-width (or simply, delineated) if for every hereditary closure $\mathcal D$ of a subclass of …
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 …