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

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• Vincent Pfenninger (University of Birmingham)
• Thursday 26 November 2020, 16:00-17:00
• https://bham-ac-uk.zoom.us/j/83022685017?pwd=L1RQclI2dmIvL2RXeUNCblpuanlBUT09.

If you have a question about this talk, please contact M.Jenssen.

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 Łuczak’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.

This talk is included in these lists:

• Combinatorics and Probability Seminar
• School of Mathematics Events
• https://bham-ac-uk.zoom.us/j/83022685017?pwd=L1RQclI2dmIvL2RXeUNCblpuanlBUT09

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