Thema der Dissertation:
Upper density problems in infinite Ramsey theory Thema der Disputation:
A proof of the Erdős-Faber-Lovász conjecture
Upper density problems in infinite Ramsey theory Thema der Disputation:
A proof of the Erdős-Faber-Lovász conjecture
Abstract:
Upper density problems in infinite Ramsey theory
Let H be an infinite graph. In a two-coloring of the edges of the complete graph on the natural numbers, what is the densest monochromatic subgraph isomorphic to H that we are guaranteed to find? We measure the density of a subgraph by the upper density of its vertex set. This question, in the particular case of the infinite path, was introduced by Erdős and Galvin. Following a recent result for the infinite path, we present bounds on the maximum density for other choices of H, including exact values for wide classes of bipartite graphs and infinite factors. A proof of the Erdős-Faber-Lovász conjecture
The Erdős-Faber-Lovász conjecture states that every linear hypergraph on n vertices admits a proper edge-coloring on at most n colors. In a recent breakthrough, Kang, Kelly, Kühn, Methuku and Osthus proved that the conjecture holds for all large enough n. In this talk we will give an overview of their proof and discuss the techniques used therein, with emphasis on the proofs of two particular cases and two stability versions of the result.
Upper density problems in infinite Ramsey theory
Let H be an infinite graph. In a two-coloring of the edges of the complete graph on the natural numbers, what is the densest monochromatic subgraph isomorphic to H that we are guaranteed to find? We measure the density of a subgraph by the upper density of its vertex set. This question, in the particular case of the infinite path, was introduced by Erdős and Galvin. Following a recent result for the infinite path, we present bounds on the maximum density for other choices of H, including exact values for wide classes of bipartite graphs and infinite factors. A proof of the Erdős-Faber-Lovász conjecture
The Erdős-Faber-Lovász conjecture states that every linear hypergraph on n vertices admits a proper edge-coloring on at most n colors. In a recent breakthrough, Kang, Kelly, Kühn, Methuku and Osthus proved that the conjecture holds for all large enough n. In this talk we will give an overview of their proof and discuss the techniques used therein, with emphasis on the proofs of two particular cases and two stability versions of the result.
Zeit & Ort
26.02.2021 | 09:30