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Matroid Theory$
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James Oxley

Print publication date: 2011

Print ISBN-13: 9780198566946

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198566946.001.0001

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Basic Definitions and Examples

Basic Definitions and Examples

Chapter:
1 Basic Definitions and Examples
Source:
Matroid Theory
Author(s):

James Oxley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566946.003.0002

Matroids can be defined in many different but equivalent ways. This chapter introduces these different axiom systems and proves their equivalence. It also presents various fundamental examples of matroids and illustrates the basic concepts in the context of these examples. The discussions cover independent sets and circuits; bases; rank; closure; geometric representations of matroids of small rank; transversal matroids; the lattice of flats; and the greedy algorithm.

Keywords:   matroids, independent sets, circuits, bases, rank, closure, geometric representations, transversal matroids, greedy algorithm, lattice of flats

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