University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Large monochromatic tight cycles in 2-edge-coloured complete 4-uniform hypergraphs

Large monochromatic tight cycles in 2-edge-coloured complete 4-uniform hypergraphs

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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 Ɓuczak’s connected matching method together with a novel auxiliary graph, which I call the blueprint. This is joint work with Allan Lo.

This talk is part of the Combinatorics and Probability Seminar series.

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