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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 Click above image for expanded view 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 $n$.

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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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 $n$.

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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