A Counter-Intuitive Correlation in a Random Tournament

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: Journal
• Year: 2011
• Where: CPC
• Authors: Sven Erick Alm, Svante Linusson
• Keywords: Complete Graph Kn, CPC 2011, Distinct Vertices, Education, Oriented Graph