Electronic ISBN:  9781470401450 
Product Code:  MEMO/118/566.E 
List Price:  $42.00 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 118; 1996; 103 ppMSC: Primary 05;
Two of the authors proved a wellknown 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.

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 halfgrid

11. Excluding $K_{\aleph _0}$

12. Dissections and treedecompositions

13. Topological trees

14. Wellfounded trees

15. Wellfounded treedecompositions


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Two of the authors proved a wellknown 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 halfgrid

11. Excluding $K_{\aleph _0}$

12. Dissections and treedecompositions

13. Topological trees

14. Wellfounded trees

15. Wellfounded treedecompositions