Feature Column

Matroids: The Value of Abstraction



6. References

Birkhoff, G., Abstract linear dependence in lattices, Amer. J. Math., 57 (1935) 800-804.

Bondy, A. and D. Welsh, Some results on transversal matroids and constructions for identically self-dual matroids, Quart. J. Math. Oxford Ser., 22 (1971) 435-451.

Bonin, J. and J. Oxley, B. Servatius, (eds.), Matroid Theory, American Mathematical Society, 1996.

Brualdi, R., On fundamental transversal matroids, Proc. Amer. Math. Soc., 45 (1974) 151-156.

Bryant, V. and H. Perfect, Independence Theory in Combinatorics, Chapman and Hall, London, 1980.

Brylawski, T. and D. Kelly, Matroids and Combinatorial Geometries, Department of Mathematics, University of North Carolina, Chapel Hill, 1980.

Crapo, H. and G.-C. Rota, On the Foundations of Combinatorial Theory: Combinatorial Geometries, MIT Press, Cambridge, 1970.

Edmunds, J., A Brief Description of Matroid Theory, National Bureau of Standards, 1964.

Edmunds, J. and D. Fulkerson, Transversals and matroid partition, J. Res. Nat. Bur. Standards, 69B (1965) 147-153.

Graver, J., Lectures on the Theory of Matroids, U. of Alberta, Edmonton, 1966.

Harary, F. and D. Welsh, Matroids versus graphs, in The Many Facets of Graph Theory, Springer-Verlag, Berlin, 1969, p. 155-170.

Holzmann, C. and P. Norton, M. Tobey, A graphical representation of matroids, SIAM J. Appl. Math., 25 (1973) 618-627.

Ingleton, A., Representation of matroids, in Combinatorial Mathematics and Its Applications, D. Welsh, (ed.), Academic Press, London, 1971.

Kung, J., (ed.), A Source Book in Matroid Theory, Birkhäuser, Boston, 1986.

Las Vergnas, M., Sur les systèmes de représentants distincts d'une famille d'ensembles, C.R. Acad. Sci. Paris Sér. A-B 270 (1970) A501-503.

Lawler, E., Combinatorial optimization: networks and matroids, Holt. Rinehart, and Winston, New York, 1976.

Mac Lane, S., Some interpretation of abstract linear dependence in terms of projective geometry, Amer. J. Math., 58 (1936) 236-240.

Maurer, S., Matrix generalizations of some theorems on trees, cycles and cocyles in graphs, SIAM J. Appl. Math., 30 (1976) 148.

Mirsky, L. Transversal Theory, Academic Press, New York, 1971.

Oxley, J. Matroid Theory, Oxford University Press, Oxford, 1992.

Oxley, J., What is a matroid? (preprint.)

Rado, R., A theorem on independence relations, Quart. J. Math., 13 (1942) 83-89.

Recski, A., Matroid Theory and its Applications, Springer-Verlag, Berlin, 1989.

Seymour, P. The matroids with the max-flow min-cut property, J. Comb. Theory, Series B, 23 (1977) 189-222.

Seymour, P., Matroid representation over GF(3), J. Comb Theory, Series B, 26 (1979) 159-173.

Seymour, P., Decomposition of regular matroids, J. Comb. Theory, Series B, 28 (1980) 305-359.

Seymour, P., Recognizing graphic matroids, Combinatorica 1 (1981) 75-78.

Seymour, P., On minors of non-binary matroids, Combinatorica 1 (1981) 387-394.

Sugihara, K., Machine Interpretation of Line Drawings, MIT Press, Cambridge U. Press, Cambridge, 1986.

Truemper, K., Matroid Decomposition, Academic Press, Boston, 1992.

Tutte, W., Matroids and graphs, Trans. Amer. Math. Soc., 88 (1958) 527-552.

Tutte, W., An algorithm for determining whether a given binary matroid is graphic, Proc. Amer. Math. Soc., 11 (1960) 905-917.

Tutte, W., Lectures on Matroids, J. Res. Nat. Bur. Standards, 69B (1965) 1-47.

Tutte, W., Introduction to the Theory of Matroids, Elsevier, New York, 1971.

Von Randow, R., Introduction to the Theory of Matroids, Lecture Notes in Economics and Mathematical Systems, Volume 109, Springer-Verlag, Berlin, 1975.

Welsh, D., Matroid Theory, Academic Press, London, 1976.

White, N. (ed.), Theory of Matroids, Cambridge U. Press, Cambridge, 1986.

White, N. (ed.), Combinatorial Geometries, Cambridge U. Press, Cambridge, 1987.

White, N. (ed.), Matroid Applications, Cambridge U. Press, Cambridge, 1992.

Whitely, W., Some matroids from discrete applied geometry, in Matroid Theory, J. Bonin, j. Oxley, and B. Servatius, (eds.), American Mathematical Society, Providence, 1996, p. 171-311.

Whitney, H., On the abstract properties of linear dependence, Amer. J. Math., 57 (1935) 509-533.

Wilson, R., An introduction to matroid theory, Amer. Math. Monthly, 80 (1973) 500-525.

Notes:

An online bibliography of books about matroids is available.

Those who can access JSTOR can find some of the papers mentioned above there.

Acknowledgment

My thanks to Professor Leroy Dickey (University of Waterloo) for calling my attention to a picture of W.T. Tutte available on the University of Waterloo web site.


  1. Introduction
  2. Vector spaces and graphs
  3. Multiple births
  4. The development of a theory of matroids
  5. Applications of matroids
  6. References

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