기초과학연구원 이산수학그룹
This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a …
We prove that if $n \geq 3$, then any family of $3n-3$ sets of matchings of size $n$ in any graph has a rainbow matching of size $n$. This improves …
Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all …
Graph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph $G$ is called $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$, but …
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 …
Corneil, Olariu, and Stewart presented a recognition algorithm for interval graphs by six graph searches. Li and Wu simplified it to only four. The great simplicity of the latter algorithm …
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 …