DATE: 10 February 2021
SPEAKER: Vincent Pfenninger
TITLE: Large monochromatic tight cycles in 2-edge-coloured complete 4-uniform
hypergraphs
ABSTRACT: A 4-uniform tight cycle is a 4-uniform hypergraph with a cyclic
ordering of its vertices such that its edges are precisely the sets of 4
consecutive vertices in the ordering. Given a 2-edge-coloured complete
4-uniform hypergraph, we consider the following two questions.
1) What is the length of the longest monochromatic tight cycle? In other words,
what is the Ramsey number for tight cycles?
2) How many tight cycles are needed to partition the vertex set? This is a
generalisation of Lehel's conjecture for graphs.
In this talk, I will highlight a common approach, which yields some asymptotic
results for these two questions. The approach is based on Ćuczak's connected
matching method together with a novel auxiliary graph, which I call the
blueprint. This is joint work with Allan Lo.