기초과학연구원 이산수학그룹
A theoretical dynamical system is a pair (X,T) where X is a compact metric space and T is a self homeomorphism of X. The topological entropy of a theoretical dynamical system (X,T), first introduced in 1965 by Adler, Konheim and McAndrew, is a nonnegative real number that measures the complexity of the system. Systems with positive …
The well-known 1-2-3 Conjecture by Karoński, Łuczak and Thomason states that the edges of any connected graph with at least three vertices can be assigned weights 1, 2 or 3 so that for each edge
In a rainbow variant of the Turán problem, we consider
A loose cycle is a cyclic ordering of edges such that every two consecutive edges share exactly one vertex. A cycle is Hamilton if it spans all vertices. A codegree of a
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. As probabilistic constructions often provide good bounds on quantities in extremal combinatorics, we say that a graph H is common if the random 2-edge-coloring asymptotically minimizes the number of monochromatic copies of H. …
How can one arrange a collection of convex sets in d-dimensional Euclidean space? This guiding question is fundamental in discrete geometry, and can be made concrete in a variety of ways, for example the study of hyperplane arrangements, embeddability of simplicial complexes, Helly-type theorems, and more. This talk will focus on the classical topic of d-representable …
An oriented graph is a digraph that does not contain a directed cycle of length two. An (oriented) graph
Take a prime power
In 1986, Robertson and Seymour proved a generalization of the seminal result of Erdős and Pósa on the duality of packing and covering cycles: A graph has the Erdős-Pósa property for minor if and only if it is planar. In particular, for every non-planar graph
The square of a graph