A Group-Theoretical Approach to Disjoint Paths in Directed Graphs (1993) [1 citations — 0 self]
by
Alexander Schrijver
CWI Quarterly
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@ARTICLE{Schrijver93agroup-theoretical,
author = {Alexander Schrijver},
title = {A Group-Theoretical Approach to Disjoint Paths in Directed Graphs},
journal = {CWI Quarterly},
year = {1993},
volume = {6},
pages = {257--266}
}
author = {Alexander Schrijver},
title = {A Group-Theoretical Approach to Disjoint Paths in Directed Graphs},
journal = {CWI Quarterly},
year = {1993},
volume = {6},
pages = {257--266}
}
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Abstract:
Introduction The k disjoint paths problem is as follows: (1) given: a graph D = (V; E) and k pairs (r 1 ; s 1 ); : : : ; (r k ; s k ) of vertices of D; find: k pairwise vertex-disjoint paths P 1 ; : : : ; P k in D, where P i runs from r i to s i (i = 1; : : : ; k). This is in general a hard problem. The problem is NP-complete (Knuth cf. [3]) even if we restrict ourselves to planar undirected graphs (Lynch [4]), assuming that k is variable. On the other hand, it is a deep result of Robertson and Seymour [6] that for each fixed
Citations
| 169 | Graph minors XIII. The disjoint paths problem – Robertson, Seymour - 1995 |
| 103 | The directed subgraph homeomorphism problem – Fortune, Hopcroft, et al. - 1980 |
| 54 | On the computational complexity of combinatorial problems. Networks – Karp - 1975 |
| 12 | The Equivalence of Theorem Proving and the Interconnection Problem – Lynch - 1975 |
| 12 | Finding k disjoint paths in a directed planar graph – Schrijver - 1994 |
| 8 | The vertex-disjoint Menger problem in planar graphs – Ripphausen-Lipa, Wagner, et al. - 1997 |
| 2 | Disjoint paths in a planar graph --- a general theorem – Ding, Schrijver, et al. - 1992 |
