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

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

Duration: This information is not available in the database

Location: OAT S15/S16/S17

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.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login