A chain theorem for matroids

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Discussion / Working Papers
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Publisher
University of Canterbury
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Date
2006
Authors
Oxley, J.
Semple, C.
Whittle, G.
Abstract

Tutte's Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a 3-connected minor N such that |E(M)| - |E(N)| = 1. Geelen and Whittle extended this theorem by showing that when M is sequentially 4-connected, the minor N can also be guaranteed to be sequentially 4-connected, that is, for every 3-separation (X, Y) of N, the set E(N) can be obtained from X or Y by successively applying the operations of closure and coclosure. Hall proved a chain theorem for a different class of 4-connected matroids, those for which every 3-separation has at most five elements on one side. This paper proves a chain theorem for those sequentially 4-connected matroids that also obey this size condition.

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ANZSRC fields of research
Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490404 - Combinatorics and discrete mathematics (excl. physical combinatorics)
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