기초과학연구원 이산수학그룹
The sphere packing problem asks for the densest packing of nonoverlapping equal-sized balls in the space. This is an old and difficult problem in discrete geometry. In this talk, we …
One interesting difference between (nondegenerate) Graph Turán problem and Hypergraph Turán problem is that the hypergraph families can have at least two very different extremal constructions. In this talk, we …
A hole in a graph $G$ is an induced cycle of length at least four, and for every hole $H$ in $G$, a vertex $h\in G\setminus H$ is called a …
A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product …
We confirm a conjecture of Gartland and Lokshtanov : if for a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no member of $\mathcal{G}$ contains a $k$-creature …
Random walks and spectral methods have had a strong influence on modern graph algorithms as evidenced by the extensive literature on the subject. In this talk, I will present how …
A conjecture of Milena Mihail and Umesh Vazirani states that the edge expansion of the graph of every $0/1$ polytope is at least one. Any lower bound on the edge expansion gives …
I will present the short proof from that for every digraph F and every assignment of pairs of integers $(r_e,q_e)_{e\in A(F)}$ to its arcs, there exists an integer $N$ such …
We introduce a novel definition of orientation on the triples of a family of pairwise intersecting planar convex sets and study its properties. In particular, we compare it to other …
An $n$-vertex graph is called $C$-Ramsey if it has no clique or independent set of size $C\log_2 n$ (i.e., if it has near-optimal Ramsey behavior). We study edge-statistics in Ramsey …