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, 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.

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