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Monochromatic cycle partitions

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  • UserShoham Letzter (University of Cambridge)
  • ClockThursday 05 March 2015, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

In 2011, Schelp introduced the idea of considering Ramsey-Turán type problems for graphs with large minimum degree. Inspired by his questions, Balogh, Barát, Gerbner, Gyárfás, and Sárközy suggested the following conjecture. Let G be a graph on n vertices with minimum degree at least 3n/4. Then for every red and blue colouring of the edges of G, the vertices of G may be partitioned into two vertex-disjoint cycles, one red and the other blue. They proved an approximate version of the conjecture, and recently DeBiasio and Nelsen obtained a stronger approximate result. We prove the conjecture exactly (for large n).

I will give an overview of the history of this problem and describe some of the tools that are used for the proof. I will finish with a discussion of possible future work for which the methods we use may be applicable.

This talk is part of the Combinatorics Seminar series.

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