Matroids are an abstraction of several combinatorial objects, among them graphs and matrices. The word matroid was coined by Whitney in 1935 in his landmark paper "On the abstract properties of linear dependence". In defining a matroid Whitney tried to capture the fundamental properties of dependence that are common to graphs and matrices. Simple matroids, that is matroids without loops and parallel elements, are frequently called combinatorial geometries. Matroid theory provides a framework in which problems in combinatorial optimization, operations research and graph theory become simpler to understand.
Here is a list of some useful books related to Matroid Theory. For a good introduction to matroids see James Oxley's book Matroid Theory. Click here for a Postscript file containing an errata and update on conjectures, problems, and references.
A Toast to Matroids by W. T. Tutte .
Home Pages of people in Matroid Theory . This page has a growing list of mathematicians working in matroid theory.
Oid - a software system for experimenting with matroids. This page has information on Oid and links to other matroid and combinatorial software.
Matroid Bibliography:
A - D,
E - H,
I - L,
M - P,
Q - T,
U - Z.
Many thanks to James Oxley for generously allowing me to post on the web all the references in his book.
Matroid Links
Joe Bonin's Introduction to Matroids
Alexandre Borovik's Coxeter Matroids
Lukas Finschi's Oriented Matroids Site
Joseph Malkevitch's Matroids: The Value of Abstraction
James Oxley's What is a Matroid?
Steve Pagano's Matroids and Signed Graphs
Lyle Ramshaw and Jim Saxe's report on Quadrangular Sets to the Budget Matroids
Neil White's page on Coxeter Matroids
Thomas Zaslavsky's Matroid Miscellany and survey of signed and gain graphs
Combinatorics Links
Vaek Chvátal's perfect papers
Ian Anderson and Iiro Honkala's lecture notes in Combinatorial Designs (39 page postscript file)
Peter Cameron's design resources and permutation groups resources
Bill Chen's Combinatorics.net and
Hyperbook of combinatorics
The combinatorial object server
Joseph Culberson's Graph Coloring Page
Joe Fields' On-line Dictionary of Combinatorics
Stephen Locke's Graph Theory and Graph Theory Books
Brendan McKay's collection of combinatorial data
John Noonan's Hyperbook of Combinatorics
Neil Robertson's Algorithmic Problems on Graph Minors
Gordon Royle's Combinatorial Catalogues
Daniel Sander's Graph Theory Resources
Neil Sloane's On-Line Encyclopedia of Integer Sequences
Neil Sloane and Gabriele Nebe's Catalogue of Lattices
Douglas Stinson and Ruizhong Wei's Bibliography on Secret Sharing Schemes and Bibliography on Authentication Codes
Robin Thomas' page on The Four Color Theorem
The Electronic Journal of Combinatorics which maintains a list of Home pages of combinatorial people and groups
Math Links
James Cargal's recommended boooks in Mathematics
Jerry Grossman's Erdös Number Project (in collaboration with Patrick Ion and Rodrigo De Castro)
Ron Knott's Fibonacci numbers and the golden section
Tutorial - interactive modules on topics in Operations Research (OR) and Management Science topics.