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

Date and Time: Thursday, September 26, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Mike Molloy (University of Toronto)

Frozen vertices in colourings of a random graph

Over the past decade, much of the work on random graph colouring, random k-SAT, and other random constraint satisfaction problems has focussed on some foundational unproven hypotheses that have arisen from statistical physics. Some of the most important such hypotheses concern the "clustering" of solutions.

In the context of colourings: It is believed that if the edge-density is sufficiently high then the colourings of a random graph can be partitioned into clusters that are, in some sense, both well-connected and well-separated. Furthermore, clusters contain a linear number of "frozen vertices", whose colours remain fixed amongst all the colourings in a cluster. The density above which such clusters appear corresponds to an "algorithmic barrier", above which no algorithm has been proven to find a colouring.

In this talk, we determine the exact value of the "freezing threshold", i.e. the edge-density at which frozen vertices appear.

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