Matroid theory /

James Oxley provides a comprehensive introduction to matroid theory, covering the very basics to more advanced topics. With over 500 exercises and proofs of major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science.

Bibliographic Details
Main Author: Oxley, J. G.
Format: eBook
Language:English
Published: Oxford ; New York : Oxford University Press, 2011.
Edition:2nd ed.
Series:Oxford graduate texts in mathematics ; 21.
Subjects:
Online Access:Connect to the full text of this electronic book

MARC

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245 1 0 |a Matroid theory /  |c James Oxley. 
250 |a 2nd ed. 
260 |a Oxford ;  |a New York :  |b Oxford University Press,  |c 2011. 
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490 1 |a Oxford graduate texts in mathematics ;  |v 21 
504 |a Includes bibliographical references (pages 608-638) and index. 
505 0 |a Machine generated contents note: 1. Basic definitions and examples -- 1.1. Independent sets and circuits -- 1.2. Bases -- 1.3. Rank -- 1.4. Closure -- 1.5. Geometric representations of matroids of small rank -- 1.6. Transversal matroids -- 1.7. The lattice of flats -- 1.8. The greedy algorithm -- 2. Duality -- 2.1. The definition and basic properties -- 2.2. Duals of representable matroids -- 2.3. Duals of graphic matroids -- 2.4. Duals of transversal matroids -- 3. Minors -- 3.1. Contraction -- 3.2. Minors of certain classes of matroids -- 3.3. The Scum Theorem, projection, and flats -- 4. Connectivity -- 4.1. Connectivity for graphs and matroids -- 4.2. Properties of matroid connectivity -- 4.3. More properties of connectivity -- 5. Graphic matroids -- 5.1. Representability -- 5.2. Duality in graphic matroids -- 5.3. Whitney's 2-Isomorphism Theorem -- 5.4. Series-parallel networks -- 6. Representable matroids -- 6.1. Projective geometries -- 6.2. Affine geometries -- 6.3. Different matroid representations -- 6.4. Constructing representations for matroids -- 6.5. Representability over finite fields -- 6.6. Regular matroids -- 6.7. Algebraic matroids -- 6.8. Characteristic sets and decidability -- 6.9. Modularity -- 6.10. Dowling geometries -- 7. Constructions -- 7.1. Series and parallel connection and 2-sums -- 7.2. Single-element extensions -- 7.3. Quotients and related operations -- 7.4.A non-commutative operation -- 8. Higher connectivity -- 8.1. Tutte's definition -- 8.2. Properties of the connectivity function -- 8.3.3-cormected matroids and 2-suins -- 8.4. Wheels and whirls -- 8.5. Tutte's Linking Theorem and its applications -- 8.6. Matroid versus graph connectivity -- 8.7. Some extremal connectivity results -- 8.8. Tutte's Wheels-and-Whirls Theorem -- 9. Binary matroids -- 9.1. Characterizations -- 9.2. Circuit and cocircuit spaces -- 9.3. The operation of 3-sum -- 9.4. Other special properties -- 10. Excluded-minor theorems -- 10.1. The characterization of regular matroids -- 10.2. The characterization of ternary matroids -- 10.3. The characterization of graphic matroids -- 10.4. Further properties of regular and graphic matroids -- 11. Submodular functions and matroid union -- 11.1. Deriving matroids from submodular functions -- 11.2. The theorems of Hall and Rado -- 11.3. Matroid union and its applications -- 11.4. Amalgams and the generalized parallel connection -- 11.5. Generalizations of delta-wye exchange -- 12. The Splitter Theorem -- 12.1. The theorem and its proof -- 12.2. Applications of the Splitter Theorem -- 12.3. Variations on the Splitter Theorem -- 13. Seymour's Decomposition Theorem -- 13.1. Overview -- 13.2. Graphic, cographic, or a special minor -- 13.3. Blocking sequences -- 13.4.R12-minors -- 14. Research in representability and structure -- 14.1. The Well-Quasi-Ordering Conjecture for Matroids -- 14.2. Branch-width -- 14.3. Rota's Conjecture and the Well-Quasi-Ordering Conjecture -- 14.4. Algorithmic consequences -- 14.5. Intertwining -- 14.6. Inequivalent representations -- 14.7. Ternary matroids -- 14.8. Stabilizers -- 14.9. Unavoidable minors -- 14.10. Growth rates -- 15. Unsolved problems -- 15.1. Representability: linear and algebraic -- 15.2. Unimodal conjectures -- 15.3. Critical problems -- 15.4. From graphs to matroids -- 15.5. Enumeration -- 15.6.G amino ids and transversal matroids -- 15.7. Excluding a uniform matroid -- 15.8. Negative correlation -- 15.9.A miscellany. 
520 8 |a James Oxley provides a comprehensive introduction to matroid theory, covering the very basics to more advanced topics. With over 500 exercises and proofs of major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science. 
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