Graph minors XV. Giant steps

Neil Robertson, P. D. Seymour

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Let G be a graph with a subgraph H drawn with high representativity on a surface Σ. When can the drawing of H be extended "up to 3-separations" to a drawing of G in Σ if we permit a bounded number (κ say) of "vortices" in the drawing of G, that is, local areas of non-planarity? (The case κ = 0 was studied in the previous paper of this series.) For instance, if there is a path in G with ends in H, far apart, and otherwise disjoint from H, then no such extension exists. We are concerned with the converse; if no extension exists, what can we infer about G? It turns out that either there is a path as above, or one of two other obstructions is present.

Original languageEnglish (US)
Pages (from-to)112-148
Number of pages37
JournalJournal of Combinatorial Theory. Series B
Issue number1
StatePublished - Sep 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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