eBook 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 |
eBook 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 118; 1996; 103 ppMSC: 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 \(n\).
ReadershipResearch mathematicians in infinite graph theory.
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Table of Contents
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Chapters
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1. Introduction
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2. Dissections
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3. Havens and minors
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4. Clustered havens of order $\aleph _0$
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5. The easy halves
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6. Divisions
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7. Long divisions
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8. Robust divisions
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9. Limited dissections
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10. Excluding the half-grid
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11. Excluding $K_{\aleph _0}$
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12. Dissections and tree-decompositions
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13. Topological trees
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14. Well-founded trees
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15. Well-founded tree-decompositions
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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.
-
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