General vertex disjoint paths in series-parallel graphs

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Abstract

Let G = (V, E) be an undirected graph and let (si,ti), 1 ≤ i ≤ k be k pairs of vertices in G. The vertex disjoint paths problem is to find k paths P1,...,Pk such that Pi connects si and ti and any two of these paths may intersect only at a common endpoint. This problem is NP-complete even for planar graphs. Robertson and Seymour proved that when k is a fixed integer this problem becomes polynomial. We present a linear time algorithm for solving the decision version of the general problem when the input graph is a series-parallel graph.

Original languageEnglish
Pages (from-to)147-164
Number of pages18
JournalDiscrete Applied Mathematics
Volume41
Issue number2
DOIs
StatePublished - 26 Jan 1993
Externally publishedYes

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