On the asymmetry of random regular graphs and random graphs

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]. © 2002 Wiley Periodicals, Inc. Random...

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Bibliographic Details
Published inRandom structures & algorithms Vol. 21; no. 3-4; pp. 216 - 224
Main Authors Kim, Jeong Han, Sudakov, Benny, Vu, Van H.
Format Journal Article
LanguageEnglish
Published New York Wiley Subscription Services, Inc., A Wiley Company 01.10.2002
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Summary: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]. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 216–224, 2002
Bibliography:istex:64B092BA57092533BE3EADA04E5BB8D4387D7496
ArticleID:RSA10054
A. Sloan fellowship
NSF Grants - No. DMS-0106589; No. CCR-9987845; No. DMS-0200357
ark:/67375/WNG-NRBBVFRX-M
UCSD - No. RB091G-VU
State of New Jersey
Website
www.math.ucsd/∼vanvu
Part of this research was done while visiting Microsoft Research.
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.10054