A Counter-Intuitive Correlation in a Random Tournament

作者:Alm Sven Erick*; Linusson Svante
来源:Combinatorics Probability & Computing, 2011, 20(1): 1-9.
DOI:10.1017/S0963548310000131

摘要

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 K(n), 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.

  • 出版日期2011-1