기초과학연구원 이산수학그룹
We propose a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a …
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 $C_2$, …
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 …
In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.
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 …
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 …
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set …
A signed graph is a graph in which each edge has a positive or negative sign. Calling two graphs switch equivalent if one can get from one to the other …
A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all …
A convex lattice polytope is the convex hull of a set of integral points. Vershik conjectured the existence of a limit shape for random convex lattice polygons, and three proofs …