Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, October 29, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Alexey Pokrovskiy

Covering coloured graphs by cycles

A conjecture of Erdős, Gyárfás, and Pyber says that the vertices of any r-edge-coloured complete graph can be covered by r vertex-disjoint monochromatic cycles. This conjecture was proved for r = 2, but turned out to be false for r at least 3. However there remain various weaker versions of the conjecture which may still hold. I will discuss how to prove a 3-colour version of it when one wants to cover the graph by paths instead of cycles.

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