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# Maintaining Matroid 3-Connectivity With Respect to a Fixed Basis

thesis

posted on 2021-11-10, 21:56 authored by Alan WilliamsWe show that for any 3-connected matroid M on a ground set of at least four elements such that M does not contain any 4-element fans, and any basis B of M, there exists a set K [is a subset of] E(M) of four distinct elements such that for all k [is an element of the set] K, si(M=k) is 3-connected whenever k [is an element of the set] B, and co(M\k) is 3-connected whenever k [is an element of the set] E(M) - B. Moreover, we show that if no other elements of E(M) - K satisfy this property, then M necessarily has path-width 3.

## History

## Copyright Date

2010-01-01## Date of Award

2010-01-01## Publisher

Te Herenga Waka—Victoria University of Wellington## Rights License

Author Retains Copyright## Degree Discipline

Mathematics## Degree Grantor

Te Herenga Waka—Victoria University of Wellington## Degree Level

Masters## Degree Name

Master of Science## Victoria University of Wellington Item Type

Awarded Research Masters Thesis## Language

en_NZ## Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research## Advisors

Whittle, Geoff## Usage metrics

## Keywords

MatroidConnectivityBasisSchool: School of Mathematics, Statistics and Operations Research010107 Mathematical Logic, Set Theory, Lattices and Universal AlgebraMarsden: 230101 Mathematical Logic, set Theory, Lattices and CombinatoricsDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceMathematical Logic, Set Theory, Lattices and Universal Algebra