기초과학연구원 이산수학그룹
We examine algorithmic extensions of two classic results of extremal combinatorics. First, the theorem of Dirac from 1952 asserts that a 2-connected graph G with the minimum vertex degree d>1, …
In 1982 Galvin, Rival, and Sands proved that in $K_{t,t}$-subgraph free graphs (t being fixed), the existence of a path of order n guarantees the existence of an induced path …
The first-order model checking problem for finite graphs asks, given a graph G and a first-order sentence $\phi$ as input, to decide whether $\phi$ holds on G. Showing the existence …
We prove that for every graph F with at least one edge there are graphs H of arbitrarily large chromatic number and the same clique number as F such that …
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. …
Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a …
We show that if $L_1$ and $L_2$ are linear transformations from $\mathbb{Z}^d$ to $\mathbb{Z}^d$ satisfying certain mild conditions, then, for any finite subset $A$ of $\mathbb{Z}^d$, \ This result corrects …
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 …