기초과학연구원 이산수학그룹
The famous Erdős-Rademacher problem asks for the smallest number of r-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value …
The cut-rank of a set X of vertices in a graph G is defined as the rank of the X×(V(G)∖X) matrix over the binary field whose (i,j)-entry is 1 if …
Computationally hard problems have been widely used to construct cryptographic primitives such as encryptions, digital signatures. For example, provably secure primitives are based on a reduction from the hardness problems. …
The fractional Helly theorem is a simple yet remarkable generalization of Helly's classical theorem on the intersection of convex sets, and it is of considerable interest to extend the fractional Helly …
Pósa's theorem states that any graph G whose degree sequence $d_1\leq \dots \leq d_n$ satisfies $d_i \geq i+1$ for all $i< n/2$ has a Hamilton cycle. This degree condition is …
A weak order is a way to rank n objects where ties are allowed. Weak orders have applications in diverse areas such as linguistics, designing combination locks, and even in …
Online list coloring and DP-coloring are generalizations of list coloring that attracted considerable attention recently. Each of the paint number, $\chi_P(G)$, (the minimum number of colors needed for an online …
For given graphs $G$ and $F$, the Turán number $ex(G,F)$ is defined to be the maximum number of edges in an $F$-free subgraph of $G$. Briggs and Cox introduced a …
Oftentimes in chromatic graph theory, precoloring techniques are utilized in order to obtain the desired coloring result. For example, Thomassen's proof for 5-choosability of planar graphs actually shows that two adjacent …
Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide whether an input graph G has a square root H that belongs to $\mathcal{H}$. We …