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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, March 10, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nina Kamcev

Bounded colorings of multipartite graphs

Let c be an edge-coloring of the complete n-vertex graph Kn. The problem of finding properly colored and rainbow Hamilton cycles in c was initiated in 1976 by Bollobás and Erdős and has been extensively studied since then. We study multipartite analogues of such questions. We give (up to a constant factor) optimal sufficient conditions for a coloring c of the complete m-partite graph to contain a properly colored or rainbow copy of a given graph G with maximum degree d. Our bounds exhibit a surprising transition in the rate of growth, showing that the problem is fundamentally different in the regimes d>>m and m>>d. Our main tool is the framework of Lu and Székely for the space of random bijections, which we extend to product spaces.

This is joint work with Benny Sudakov and Jan Volec.

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