On the asymmetry of random regular graphs and random graphs

Authors:
Jeong Han Kim;Benny Sudakov;Van H. Vu
Affiliations:
Theory Group, Microsoft Research, Redmond, Washington;Department of Mathematics, Princeton University and Institute for Advanced Study, Princeton, NJ;Department of Mathematics, UCSD, La Jolla, California
Venue:
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Year:
2002

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Abstract

This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n - 4 the random d-regular graph on n vertices almost surely has no nontrivial automorphisms. This answers an open question of N. Wormald [13].