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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

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.

• 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