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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
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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$40
Individual Members: US$24
Institutional Members: US$32
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 \(n\).

Readership

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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