Correlations for paths in random orientations of G(n,p) and G(n,m)

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Correlations for paths in random orientations of G(n, p) and G(n, m)

We study random graphs, both G(n, p) and G(n,m), with random orientations on the edges. For three fixed distinct vertices s, a, b we study the correlation, in the combined probability space, of the events {a → s} and {s → b}. For G(n, p), we prove that there is a pc = 1/2 such that for a fixed p < pc the correlation is negative for large enough n and for p > pc the correlation is positive for l...

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On Orientations and Shortest Paths

An orientation of an undirected graph is a choice of direction for each of its edges. An orientation is called ideal with respect to a given set of pairs of vertices if it does not increase the shortest-path distances between the members of any of the pairs. A polynomial-time algorithm is given for constructing an ideal orientation with respect to two given pairs and any positive edge-lengths, ...

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ژورنال

عنوان ژورنال: Random Structures & Algorithms

سال: 2011

ISSN: 1042-9832

DOI: 10.1002/rsa.20358