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A Counter-Intuitive Correlation in a Random Tournament
Published online by Cambridge University Press: 13 May 2010
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.
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