General vertex disjoint paths in series-parallel graphs

Ephraim Korach; Ady Tal

doi:10.1016/0166-218X(93)90035-M

General vertex disjoint paths in series-parallel graphs

Ephraim Korach
, Ady Tal

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let G = (V, E) be an undirected graph and let (s_i,t_i), 1 ≤ i ≤ k be k pairs of vertices in G. The vertex disjoint paths problem is to find k paths P₁,...,P_k such that P_i connects s_i and t_i 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 language	English
Pages (from-to)	147-164
Number of pages	18
Journal	Discrete Applied Mathematics
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/0166-218X(93)90035-M
State	Published - 26 Jan 1993
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/0166-218X(93)90035-M

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title = "General vertex disjoint paths in series-parallel graphs",

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.",

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AB - 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.

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General vertex disjoint paths in series-parallel graphs

Abstract

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