Graph minors. VII. Disjoint paths on a surface

@article{Robertson1988GraphMV,
  title={Graph minors. VII. Disjoint paths on a surface},
  author={Neil Robertson and Paul D. Seymour},
  journal={J. Comb. Theory, Ser. B},
  year={1988},
  volume={45},
  pages={212-254}
}
Let s1 , t,, sz, t2, ,.., sk, I~ be vertices of a graph G drawn in a surface Z. When are there k vertex-disjoint paths of G linking s, and t, (1 <i< k)? We study sufficient conditions-for instance, it sufftces that G is connected and “uses up” the surface adequately, and all the s,‘s and 1,‘s are mutually “far apart.” Our results are applied to yield a polynomially bounded algorithm to solve the problem for fixed C and k. d 1988 Academic Press, Inc. 

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