Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Wednesday, June 28, 2017, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Marlo Eugster (Master's thesis)

It was proven by Erdős, Gyárfás and Pyber, that the n vertices of a complete graph, whose edges are coloured in t colours, can be covered by f(t) many monochromatic cycles. The focus of my Master Thesis is the case where we are restricted to choose monochromatic cycles of at most s < t different colours.

The main result of my thesis is that we need at most O(n^{1/r}) many cycles, where r = 2s - t + 2, to cover all vertices if t/2 < = s < t. This result is asymptotically optimal. In case s < t/2, there exist colourings such that we need a linear (in n) amount of cycles. This talk will mainly focus on the proofs of these results. I will also shortly talk about the same problem for graphs other than the complete graph.

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