The structure of 2-separations of infinite matroids

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• 作者：Elad Aigner-Horev^a ; Reinhard Diestel^b ; ; Luke Postle^c
• 关键词：Infinite ; Matroid ; Tree-decomposition ; Tutte ; Cunningham ; Edmonds ; Seymour ; 2-separation ; 3-connected
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：116
• 期：Complete
• 页码：25-56
• 全文大小：601 K

文摘

Generalizing a well known theorem for finite matroids, we prove that for every (infinite) connected matroid M there is a unique tree T such that the nodes of T correspond to minors of M that are either 3-connected or circuits or cocircuits, and the edges of T correspond to certain nested 2-separations of M. These decompositions are invariant under duality.