Preliminaries |
Basic definitions and examples / 1: |
Independent sets and circuits / 1.1: |
Bases / 1.2: |
Rank / 1.3: |
Closure / 1.4: |
Geometric representations of matroids of small rank / 1.5: |
Transversal matroids / 1.6: |
The lattice of flats / 1.7: |
The greedy algorithm / 1.8: |
Duality / 2: |
The definition and basic properties / 2.1: |
Duals of representable matroids / 2.2: |
Duals of graphic matroids / 2.3: |
Duals of transversal matroids / 2.4: |
Minors / 3: |
Contraction / 3.1: |
Minors of certain classes of matroids / 3.2: |
The Scum Theorem, projection, and flats / 3.3: |
Connectivity / 4: |
Connectivity for graphs and matroids / 4.1: |
Properties of matroid connectivity / 4.2: |
More properties of connectivity / 4.3: |
Graphic matroids / 5: |
Representability / 5.1: |
Duality in graphic matroids / 5.2: |
Whitney's 2-Isomorphism Theorem / 5.3: |
Series-parallel networks / 5.4: |
Representable matroids / 6: |
Projective geometries / 6.1: |
Affine geometries / 6.2: |
Different matroid representations / 6.3: |
Constructing representations for matroids / 6.4: |
Representability over finite fields / 6.5: |
Regular matroids / 6.6: |
Algebraic matroids / 6.7: |
Characteristic sets and decidability / 6.8: |
Modularity / 6.9: |
Dowling geometries / 6.10: |
Constructions / 7: |
Series and parallel connection and 2-sums / 7.1: |
Single-element extensions / 7.2: |
Quotients and related operations / 7.3: |
A non-commutative operation / 7.4: |
Higher connectivity / 8: |
Tutte's definition / 8.1: |
Properties of the connectivity function / 8.2: |
3-connected matroids and 2-sums / 8.3: |
Wheels and whirls / 8.4: |
Tutte's Linking Theorem and its applications / 8.5: |
Matroid versus graph connectivity / 8.6: |
Some extremal connectivity results / 8.7: |
Tutte's Wheels-and-Whirls Theorem / 8.8: |
Binary matroids / 9: |
Characterizations / 9.1: |
Circuit and cocircuit spaces / 9.2: |
The operation of 3-sum / 9.3: |
Other special properties / 9.4: |
Excluded-minor theorems / 10: |
The characterization of regular matroids / 10.1: |
The characterization of ternary matroids / 10.2: |
The characterization of graphic matroids / 10.3: |
Further properties of regular and graphic matroids / 10.4: |
Submodular functions and matroid union / 11: |
Deriving matroids from submodular functions / 11.1: |
The theorems of Hall and Rado / 11.2: |
Matroid union and its applications / 11.3: |
Amalgams and the generalized parallel connection / 11.4: |
Generalizations of delta-wye exchange / 11.5: |
The Splitter Theorem / 12: |
The theorem and its proof / 12.1: |
Applications of the Splitter Theorem / 12.2: |
Variations on the Splitter Theorem / 12.3: |
Seymour's Decomposition Theorem / 13: |
Overview / 13.1: |
Graphic, cographic, or a special minor / 13.2: |
Blocking sequences / 13.3: |
Research in representability and structure / 13.4: |
The Well-Quasi-Ordering Conjecture for Matroids / 14.1: |
Branch-width / 14.2: |
Rota's Conjecture and the Well-Quasi-Ordering Conjecture / 14.3: |
Algorithmic consequences / 14.4: |
Intertwining / 14.5: |
Inequivalent representations / 14.6: |
Ternary matroids / 14.7: |
Stabilizers / 14.8: |
Unavoidable minors / 14.9: |
Growth rates / 14.10: |
Unsolved problems / 15: |
Representability: linear and algebraic / 15.1: |
Unimodal conjectures / 15.2: |
Critical problems / 15.3: |
From graphs to matroids / 15.4: |
Enumeration / 15.5: |
Gammoids and transversal matroids / 15.6: |
Excluding a uniform matroid / 15.7: |
Negative correlation / 15.8: |
A miscellany / 15.9: |
References |
Appendix: Some interesting matroids |
List of tables |
Notation |
Index |
Preliminaries |
Basic definitions and examples / 1: |
Independent sets and circuits / 1.1: |