## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, July 28, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Henning Thomas

## Avoiding Monochromatic Giants in Edge-Colorings of Random Graphs

We are given a random graph $G_{n,m}$ (a graph drawn uniformly at random from all graphs on $n$ vertices with exactly $m$ edges) and a random partition of its edges into sets of size $r$, where $r$ is a fixed constant. We call an $r$-coloring of its edges valid if it uses each of the $r$ colors exactly once in every $r$-set. Our goal now is to find a valid $r$-edge-coloring in which no color class induces a component of size $\Omega(n)$ -- a so called `giant component'. We prove that for every $r \geq 2$, the threshold for the existence of such a coloring coincides with the threshold for $r$-orientability found by Cain, Sanders, and Wormald (SODA 07), and independently by Fernholz and Ramachandran (SODA 07).

Joint work with Reto Spöhel and Angelika Steger.

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