Paper Info
Title
Random Colourings and Automorphism Breaking in Locally Finite Graphs.
Abstract
A colouring of a graph G is called distinguishing if its stabilizer in Aut G is trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We study properties of random 2-colourings of locally finite graphs and show that the stabilizer of such a colouring is almost surely nowhere dense in Aut G and a null set with respect to the Haar measure on the automorphism group. We also investigate random 2-colourings in several classes of locally finite graphs where the existence of a distinguishing 2-colouring has already been established. It turns out that in all of these cases a random 2-colouring is almost surely distinguishing.
Year
DOI
Venue
2013
10.1017/S0963548313000382
COMBINATORICS PROBABILITY & COMPUTING
Field
DocType
Volume
Null set,Discrete mathematics,Random regular graph,Combinatorics,Nowhere dense set,Random graph,Vertex (geometry),Haar measure,Automorphism,Almost surely,Mathematics
Journal
22
Issue
ISSN
Citations 
6
0963-5483
1
PageRank 
References 
Authors
0.39
0
1
Name
Order
Citations
PageRank
Florian Lehner1217.24