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On the Diameter of Random Cayley Graphs of the Symmetric Group

Published online by Cambridge University Press:  12 September 2008

L. Babai  and
G. L. Hetyei
L. Babai
Affiliation:
Department of Computer Science, University of Chicago, 1100 E 58th St, Chicago IL 60637–1504 and Eötvös University, Budapest, Hungary E-mail: [email protected]
G. L. Hetyei
Affiliation:
Department of Mathematics, M.I.T., Cambridge MA 02139 E-mail: [email protected]
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Abstract

Let σ, π be two permutations selected at random from the uniform distribution on the symmetric group Sn. By a result of Dixon [5], the subgroup G generated by σ, π is almost always (i.e. with probability approaching 1 as n → ∞) either Sn or the alternating group An. We prove that the diameter of the Cayley graph of G defined by {σ, π} is almost always not greater than exp ((½ + o(l)). (In n)2).

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 201 - 208
Copyright
Copyright © Cambridge University Press 1992

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References

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