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Excluding Infinite Clique Minors
Neil Robertson, Ohio State University, Columbus, OH, Paul Seymour, Bellcore, Morristown, NJ, and Robin Thomas, Georgia Institute of Technology, Atlanta, GA

Memoirs of the American Mathematical Society
1996; 103 pp; softcover
Volume: 118
ISBN-10: 0-8218-0402-2
ISBN-13: 978-0-8218-0402-5
List Price: US$42
Individual Members: US$25.20
Institutional Members: US$33.60
Order Code: MEMO/118/566
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Two of the authors proved a well-known conjecture of K. Wagner, that in any infinite set of finite graphs there are two graphs so that one is a minor of the other. A key lemma was a theorem about the structure of finite graphs that have no \(K_n\) minor for a fixed integer \(n\). Here, the authors obtain an infinite analog of this lemma--a structural condition on a graph, necessary and sufficient for it not to contain a \(K_n\) minor, for any fixed infinite cardinal \(n\).


Research mathematicians in infinite graph theory.

Table of Contents

  • Introduction
  • Dissections
  • Havens and minors
  • Clustered havens of order \(\aleph _0\)
  • The easy halves
  • Divisions
  • Long divisions
  • Robust divisions
  • Limited dissections
  • Excluding the half-grid
  • Excluding \(K_{\aleph _0}\)
  • Dissections and tree-decompositions
  • Topological trees
  • Well-founded trees
  • Well-founded tree-decompositions
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