English

The structure of random automorphisms of the random graph

Logic 2018-08-21 v1

Abstract

We give a complete description of the size of the conjugacy classes of the automorphism group of the random graph with respect to Christensen's Haar null ideal. It is shown that every non-Haar null class contains a translated copy of a nonempty portion of every compact set and that there are continuum many non-Haar null conjugacy classes. Our methods also yield a new proof of an old result of Truss.

Keywords

Cite

@article{arxiv.1808.06121,
  title  = {The structure of random automorphisms of the random graph},
  author = {Udayan B. Darji and Márton Elekes and Kende Kalina and Viktor Kiss and Zoltán Vidnyánszky},
  journal= {arXiv preprint arXiv:1808.06121},
  year   = {2018}
}

Comments

Most of this work previously appeared in the first version of the paper arXiv:1705.07593 which was split into 3 articles