Tree-width and planar minors

Alexander Leaf, Paul Seymour

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Robertson and the second author [7] proved in 1986 that for all h there exists f(h) such that for every h-vertex simple planar graph H, every graph with no H-minor has tree-width at most f(h); but how small can we make f(h)? The original bound was an iterated exponential tower, but in 1994 with Thomas [9] it was improved to 2O(h5); and in 1999 Diestel, Gorbunov, Jensen, and Thomassen [3] proved a similar bound, with a much simpler proof. Here we show that f(h)=2O(hlog(h)) works. Since this paper was submitted for publication, Chekuri and Chuzhoy [2] have announced a proof that in fact f(h) can be taken to be O(h100).

Original languageEnglish (US)
Pages (from-to)38-53
Number of pages16
JournalJournal of Combinatorial Theory. Series B
StatePublished - Mar 1 2015

All Science Journal Classification (ASJC) codes

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


  • Graph minors
  • Tree-width


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