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Excluding Infinite Clique Minors
 
Neil Robertson Ohio State University
Paul Seymour Bellcore
Robin Thomas Georgia Institute of Technology
Front Cover for Excluding Infinite Clique Minors
Available Formats:
Electronic ISBN: 978-1-4704-0145-0
Product Code: MEMO/118/566.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $25.20
Front Cover for Excluding Infinite Clique Minors
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  • Front Cover for Excluding Infinite Clique Minors
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Excluding Infinite Clique Minors
Neil Robertson Ohio State University
Paul Seymour Bellcore
Robin Thomas Georgia Institute of Technology
Available Formats:
Electronic ISBN:  978-1-4704-0145-0
Product Code:  MEMO/118/566.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $25.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1181996; 103 pp
    MSC: Primary 05;

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. Dissections
    • 3. Havens and minors
    • 4. Clustered havens of order $\aleph _0$
    • 5. The easy halves
    • 6. Divisions
    • 7. Long divisions
    • 8. Robust divisions
    • 9. Limited dissections
    • 10. Excluding the half-grid
    • 11. Excluding $K_{\aleph _0}$
    • 12. Dissections and tree-decompositions
    • 13. Topological trees
    • 14. Well-founded trees
    • 15. Well-founded tree-decompositions
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Volume: 1181996; 103 pp
MSC: Primary 05;

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.

  • Chapters
  • 1. Introduction
  • 2. Dissections
  • 3. Havens and minors
  • 4. Clustered havens of order $\aleph _0$
  • 5. The easy halves
  • 6. Divisions
  • 7. Long divisions
  • 8. Robust divisions
  • 9. Limited dissections
  • 10. Excluding the half-grid
  • 11. Excluding $K_{\aleph _0}$
  • 12. Dissections and tree-decompositions
  • 13. Topological trees
  • 14. Well-founded trees
  • 15. Well-founded tree-decompositions
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