István Tomon, Configurations of boxes
Room B332 IBS (기초과학연구원)Configurations of axis-parallel boxes in
Configurations of axis-parallel boxes in
We consider the spanning tree embedding problem in dense graphs without bipartite holes and sparse graphs. In 2005, Alon, Krivelevich and Sudakov asked for determining the best possible spectral gap forcing an
Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular, that for every graph H, the class of graphs containing no H-pivot-minor is 𝜒-bounded, and also satisfies the (strong) Erdős-Hajnal property.
In 2006, Tao established the Gaussian counterpart of the celebrated Green-Tao theorem on arithmetic progressions of primes. In this talk, I will explain the extension of Tao's theorem and the Green-Tao theorem to the case of general number fields. Our combinatorial tool is the relative hypergraph removal lemma by Conlon-Fox-Zhao. I will discuss the difficulties …
For a given graph
In many different areas of mathematics (such as number theory, discrete geometry, and combinatorics), one is often presented with a large "unstructured" object, and asked to find a smaller "structured" object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that …
The Ramsey number
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