Graph Minors .XII. Distance on a Surface

Neil Robertson, P. D. Seymour

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


Let Γ a graph drawn on a connected surface ∑ which is not a sphere. It is “θ-representative” if every non-null-homotopic closed curve meets Γ at least θ times. Also, Γ defines a metric on ∑, discussed in an earlier paper. Our objective here is to study the effect on the metric and on the “representativeness” of making local changes in the drawing or in the surface. We also reformulate more compactly the main theorem of an earlier paper in terms of this metric. These are lemmas to be used later.

Original languageEnglish (US)
Pages (from-to)240-272
Number of pages33
JournalJournal of Combinatorial Theory, Series B
Issue number2
StatePublished - Jul 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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