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A Counter-Intuitive Correlation in a Random Tournament

Published online by Cambridge University Press:  13 May 2010

SVEN ERICK ALM  and
SVANTE LINUSSON
SVEN ERICK ALM
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06, Uppsala, Sweden (e-mail: sea@math.uu.se)
SVANTE LINUSSON
Affiliation:
Department of Mathematics, KTH – Royal Institute of Technology, SE-100 44, Stockholm, Sweden (e-mail: linusson@math.kth.se)
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Abstract

Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertices in V. We study the correlation between the events {a → s} and {s → b}. We show that, counter-intuitively, when G is the complete graph Kn, n ≥ 5, then the correlation is positive. (It is negative for n = 3 and zero for n = 4.) We briefly discuss and pose problems for the same question on other graphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 1 , January 2011 , pp. 1 - 9
Copyright
Copyright © Cambridge University Press 2010

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References

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