Wild triangles in 3-connected matroids

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dc.contributor.authorOxley, J.
dc.contributor.authorSemple, C.
dc.contributor.authorWhittle, G.
dc.date.accessioned2016-05-26T01:53:00Z
dc.date.available2016-05-26T01:53:00Z
dc.date.issued2006en
dc.description.abstractTutte's Triangle Lemma proves that if {a, b, c} is a triangle in a 3-connected matroid and neither M\a nor M\b is 3-connected, then M has a triad that contains a and exactly one of b and c. Hence {a, b, c} is contained in a fan of M with at least four elements. In this paper we ask for a somewhat stronger conclusion. When is it that, for each t in { a, b, c}, either M\t is not 3-connected, or M\t has a 3-separation that is not equivalent to a 3-separation induced by M? The main result describes the structure of M relative to { a, b, c} when this occurs. This theorem generalizes a result of Geelen and Whittle for sequentially 4-connected matroids. The motivation for proving this result was for use as an inductive tool for connectivity results aimed at representability questions. In particular, Geelen, Gerards, and Whittle use it in their proof of Kahn's Conjecture for 4-connected matroids.en
dc.identifier.issn1172-8531
dc.identifier.urihttp://hdl.handle.net/10092/12206
dc.language.isoen
dc.publisherUniversity of Canterburyen
dc.rightsAll Rights Reserveden
dc.rights.urihttps://canterbury.libguides.com/rights/theses
dc.subject.anzsrcFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490404 - Combinatorics and discrete mathematics (excl. physical combinatorics)en
dc.titleWild triangles in 3-connected matroidsen
dc.typeDiscussion / Working Papers
uc.collegeFaculty of Engineering
uc.departmentSchool of Engineeringen
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