@MISC{Frieze00edge-disjointpaths, author = {Alan M. Frieze}, title = { Edge-Disjoint Paths in Expander Graphs}, year = {2000} }

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Abstract

Given a graph G = (17, E) and a set of t ¢ pairs of vertices in V, we are interested in finding for each pair (hi, b~), a path connecting ai to bi, such that the set of t ¢ paths so found is edge-disjoint. (For arbitrary graphs the problem is AfT~-complete, although it is in 7 ~ if n is fixed.) We present a polynomial time randomized algo-rithm for finding edge disjoint paths in an r-regular ex-pander graph G. We show that if G has sufficiently strong expansion properties and r is sufficiently large then all sets of n = g~(n/logn) pairs of vertices can be joined. This is within a constant factor of best possible.