Splitting an Expander Graph

Let G=(V,E) be an r-regular expander graph. Certain algorithms for finding edge disjoint paths require that its edges be partitioned into E=E1?E2?···?Ek so that the graphs Gi=(V,Ei) are each expanders. In this paper we give a nonconstructive proof of the existence a very good split plus an algorithm for finding a partition better than that given in A. Z. Broder, A. M. Frieze, and E. Upfal (SIAM J. Comput.23 (1994), 976?989).

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