기초과학연구원 이산수학그룹
In 1975, Erdős asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, …
The twin-width of a graph G can be defined as the least integer d such that there is a sequence of length |V(G)| of (strictly) coarser and coarser partitions of …
We show that that the maximum number of of edges in a $3$-uniform hypergraph without a Berge-cycle of length four is at most $(1+o(1)) \frac{n^{3/2}}{\sqrt{10}}$. This improves earlier estimates by …
A pure pair in a graph G is a pair of subsets A, B of the vertex set of G such that in G, either all of the edges or …
In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.
For a graph G and an integer d, the dth power of G is the graph $G^d$ on the same vertex set as G where two vertices are considered adjacent …
Ordered Ramsey numbers were introduced in 2014 by Conlon, Fox, Lee, and Sudakov. Their results included upper bounds for general graphs and lower bounds showing separation from classical Ramsey numbers. We …
A graph $G$ is semilinear of bounded complexity if the vertices of $G$ are elements of $\mathbb{R}^{d}$, and the edges of $G$ are defined by the sign patterns of $t$ …
Bouchet introduced isotropic systems in 1983 unifying some combinatorial features of binary matroids and 4-regular graphs. The concept of isotropic system is a useful tool to study vertex-minors of graphs …
Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that typically occur together. They can thereby discover, relate, and structure …