Memoirs of the American Mathematical Society 1996; 103 pp; softcover Volume: 118 ISBN10: 0821804022 ISBN13: 9780821804025 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/118/566
 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 lemmaa 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  Introduction
 Dissections
 Havens and minors
 Clustered havens of order \(\aleph _0\)
 The easy halves
 Divisions
 Long divisions
 Robust divisions
 Limited dissections
 Excluding the halfgrid
 Excluding \(K_{\aleph _0}\)
 Dissections and treedecompositions
 Topological trees
 Wellfounded trees
 Wellfounded treedecompositions
