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SUMMARY:Monochromatic cycle partitions - Shoham Letzter (University of Cam
 bridge)
DTSTART:20150305T143000Z
DTEND:20150305T153000Z
UID:TALK57339@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:In 2011\, Schelp introduced the idea of considering Ramsey-Tur
 án type problems for graphs with large minimum degree. Inspired by his qu
 estions\, Balogh\, Barát\, Gerbner\, Gyárfás\, and Sárközy suggested 
 the following\nconjecture. Let G be a graph on n vertices with minimum deg
 ree 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 conj
 ecture\, and recently DeBiasio and Nelsen obtained a stronger approximate 
 result. We prove the conjecture exactly (for large n).\n\nI will give an o
 verview 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 futur
 e work for which the methods we use may be applicable.\n
LOCATION:MR12
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