Graph minors. VII. Disjoint paths on a surface

Neil Robertson; P. D. Seymour

doi:10.1016/0095-8956(88)90070-6

Graph minors. VII. Disjoint paths on a surface

Neil Robertson, P. D. Seymour

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

131 Scopus citations

Abstract

Let s₁, t₁, s₂, t₂, ..., s_k, t_k be vertices of a graph G drawn in a surface Σ. When are there k vertex-disjoint paths of G linking s_i and t_i (1 ≤ i ≤ k)? We study sufficient conditions-for instance, it suffices that G is connected and "uses up" the surface adequately, and all the s_i's and t_j's are mutually "far apart." Our results are applied to yield a polynomially bounded algorithm to solve the problem for fixed Σ and k.

Original language	English (US)
Pages (from-to)	212-254
Number of pages	43
Journal	Journal of Combinatorial Theory, Series B
Volume	45
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(88)90070-6
State	Published - Oct 1988
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(88)90070-6

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AB - Let s1, t1, s2, t2, ..., sk, tk be vertices of a graph G drawn in a surface Σ. When are there k vertex-disjoint paths of G linking si and ti (1 ≤ i ≤ k)? We study sufficient conditions-for instance, it suffices that G is connected and "uses up" the surface adequately, and all the si's and tj's are mutually "far apart." Our results are applied to yield a polynomially bounded algorithm to solve the problem for fixed Σ and k.

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Graph minors. VII. Disjoint paths on a surface

Abstract

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