Highly Influenced

# 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} }

- Published 1988 in J. Comb. Theory, Ser. B
DOI:10.1016/0095-8956(88)90070-6

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.