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Connections in Randomly Oriented Graphs

Published online by Cambridge University Press:  06 December 2016

BHARGAV NARAYANAN
BHARGAV NARAYANAN*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK (e-mail: b.p.narayanan@dpmms.cam.ac.uk)
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Abstract

Given an undirected graph G, let us randomly orient G by tossing independent (possibly biased) coins, one for each edge of G. Writing a → b for the event that there exists a directed path from a vertex a to a vertex b in such a random orientation, we prove that for any three vertices s, a and b of G, we have ℙ(s → a ∩ s → b) ⩾ ℙ(s → a) ℙ(s → b).

Keywords

Primary 60C05Secondary 60K35
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Special Issue 4: Special Issue: Oberwolfach Workshop , July 2018 , pp. 667 - 671
Copyright
Copyright © Cambridge University Press 2016 

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