Graph minors. V. Excluding a planar graph

Neil Robertson, P. D. Seymour

Research output: Contribution to journalArticle

386 Scopus citations

Abstract

We prove that for every planar graph H there is a number w such that every graph with no minor isomorphic to H can be constructed from graphs with at most w vertices, by piecing them together in a tree structure. This has several consequences; for example, it implies that: (i) if A is a set of graphs such that no member is isomorphic to a minor of another, and some member of A is planar, then A is finite; (ii) for every fixed planar graph H there is a polynomial time algorithm to test if an arbitrary graph has a minor isomorphic to H; (iii) there is a generalization of a theorem of Erdös and Pósa (concerning the maximum number of disjoint circuits in a graph) to planar structures other than circuits.

Original languageEnglish (US)
Pages (from-to)92-114
Number of pages23
JournalJournal of Combinatorial Theory, Series B
Volume41
Issue number1
DOIs
StatePublished - Jan 1 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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