Jozef Skokan, Separating the edges of a graph by a linear number of paths
Room B332 IBS (기초과학연구원)Recently, Letzter proved that any graph of order n contains a collection P of
Recently, Letzter proved that any graph of order n contains a collection P of
Tree decompositions are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. Tree decompositions …
We study the fundamental problem of finding small dense subgraphs in a given graph. For a real number
We define new graph parameters, called flip-width, that generalize treewidth, degeneracy, and generalized coloring numbers for sparse graphs, and clique-width and twin-width for dense graphs. The flip-width parameters are defined using variants of the Cops and Robber game, in which the robber has speed bounded by a fixed constant r∈N∪{∞}, and the cops perform flips …
The Erdős-Sós conjecture states that the maximum number of edges in an
A graph class
An archetype problem in extremal combinatorics is to study the structure of subgraphs appearing in different classes of (hyper)graphs. We will focus on such embedding problems in uniformly dense hypergraphs. In precise, we will mention the uniform Turan density of some hypergraphs.
Consider the following hat guessing game:
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