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# Tangles, Trees and Flowers

thesis

posted on 2021-11-10, 23:47 authored by Clark, BenA tangle of order k in a connectivity function λ may be thought of as a "k-connected component" of λ. For a connectivity function λ and a tangle in λ of order k that satisfies a certain robustness condition, we describe a tree decomposition of λ that displays, up to a certain natural equivalence, all of the k-separations of λ that are non-trivial with respect to the tangle. In particular, for a tangle in a matroid or graph of order k that satisfies a certain robustness condition, we describe a tree decomposition of the matroid or graph that displays, up to a certain natural equivalence, all of the k- separations of the matroid or graph that are non-trivial with respect to the tangle.

## History

## Copyright Date

2011-01-01## Date of Award

2011-01-01## 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

MatroidConnectivityTanglesSchool: 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

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