Graph minors. XVIII. Tree-decompositions and well-quasi-ordering

Neil Robertson, Paul Seymour

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We prove the following result. Suppose that for every graph G in a class C of graphs, and for every "highly connected component" of G, there is a decomposition of G of a certain kind centred on the component. Then C is well-quasi-ordered by minors; that is, in any infinite subset of C there are two graphs, one a minor of the other. This is another step towards Wagner's conjecture.

Original languageEnglish (US)
Pages (from-to)77-108
Number of pages32
JournalJournal of Combinatorial Theory. Series B
Issue number1
StatePublished - Sep 2003

All Science Journal Classification (ASJC) codes

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


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