by Thomas Zaslavsky
A list of places where you can get introduced to matroid theory at any level you wish.
Some open problems.
Matroid Theory: Where to Find It Out
Speedy easy introduction:
Short technical introductionss:
- Robin J. Wilson, "An introduction to matroid theory",
American Mathematical Monthly Vol. 80 (1973), pp. 500-525.
- Robin J. Wilson, "Matroid theory",
Ch. 9 of Introduction to Graph Theory,
Academic Press, New York-London, 1972;
2nd edn., Academic Press, New York-London, 1979;
3rd edn., Longman, London, and Wiley, New York, 1985.
Translated into Russian (1977; 1st edn.) and Polish (1985; 2nd edn.).
For a thorough introduction:
- James Oxley, Matroid Theory, Oxford University Press, Oxford, 1992.
The best introductory book. An exceptionally fine textbook. It doesn't cover everything (which would have been impossible); see the next two items for articles that make up the major omission.
- Thomas Zaslavsky, "The Möbius function and the characteristic
polynomial", Ch. 7 in: White, Theory of Matroids.
Introduces an important aspect omitted by Oxley.
- Thomas Brylawski and James Oxley,
"The Tutte polynomial and its applications",
Ch. 6 in: White, Matroid Applications.
Much more of the same important aspect omitted by Oxley, extending Zaslavsky's chapter.
- Henry Crapo, "Examples and basic concepts", Ch. 1 in: White, Theory of Matroids.
- Georgio Nicoletti and Neil White, "Axiom systems",
Ch. 2 in: White, Theory of Matroids.
An overview of many of the multiplicity of "cryptomorphisms"
(equivalent but seemingly wildly different ways to define matroids);
an antidote to the "Let (E, X) be a matroid" style of pseudo-definition.
Advanced books and articles (very selective):
- Joseph P.S. Kung, "Extremal matroid theory", in: Neil Robertson and Paul Seymour, eds., Graph Structure Theory (Proc. Conf., Seattle, 1991), pp. 21-61. Contemporary Math., Vol. 147. American Mathematical Society, Providence, R.I., 1993.
The founding paper.
- Joseph P.S. Kung, "Critical problems", in: Joseph E. Bonin, James G. Oxley, and Brigitte Servatius, eds., Matroid Theory (Proc. Conf, Seattle, 1995), pp. 1-127. Contemporary Math., Vol. 197. American Mathematical Society, Providence, R.I., 1996.
- Neil White, ed., Theory of Matroids,
Cambridge University Press, Cambridge, 1986.
- Neil White, ed., Combinatorial Geometries,
Cambridge University Press, Cambridge, 1987.
Special topics and special types of matroids.
- Neil White, ed., Matroid Applications,
Cambridge University Press, Cambridge, 1992.
Highly specialized topics, except for Ch. 6 (see above). Most important:
Anders Björner, "Homology and shellability of matroids
and geometric lattices", Ch. 7;
Anders Björner and Günter M. Ziegler,
"Introduction to greedoids", Ch. 8.
- D.J.A. Welsh, Matroid Theory,
Academic Press, London, 1976.
A thorough survey of the state of the theory at that time;
out of date but still a valuable reference, not superseded.
Important related topic:
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Last modified 2001 Aug 23
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