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The dependence graph for bases in matroids. (English) Zbl 0366.05024


MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05C99 Graph theory
68W99 Algorithms in computer science
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References:

[1] Brualdi, R. A., Comments on bases in dependence structures, Bull. Austral. Math. Soc., 2, 161-167 (1969) · Zbl 0172.30703
[2] Cunningham, W. H., A combinatorial decomposition theory, (Ph.D. Thesis (1974), Univ. of Waterloo: Univ. of Waterloo Waterloo, Ont) · Zbl 0385.05022
[3] Edmonds, J., Paths, trees and flowers, Can. J. Math., 17, 449-467 (1965) · Zbl 0132.20903
[4] Harary, F., Graph Theory (1969), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0797.05064
[5] Ingleton, A. W.; Piti, M. J., Gammoids and transversal matroids, J. Combinatorial Theory, 15, B, 51-68 (1973) · Zbl 0264.05021
[6] Karp, R. M., Reducibility among combinatorial problems, (Complexity of Computer Computations (1972), Plenum Press: Plenum Press New York) · Zbl 0366.68041
[7] Knuth, D. E., The asymptotic number of geometries, J. Combinatorial Theory, 16, 398-400 (1974) · Zbl 0278.05010
[8] S. Krogdahl, A combinatorial base for some optimal matroid intersection algorithms, Stanford Computer Science Department Report STAN-CS-74-468, Stanford Univ., Stanford, CA.; S. Krogdahl, A combinatorial base for some optimal matroid intersection algorithms, Stanford Computer Science Department Report STAN-CS-74-468, Stanford Univ., Stanford, CA.
[9] Krogdahl, S., Matroid intersection with lower bounds, (Computer Science Reports (1976), Univ. of Tromsø: Univ. of Tromsø Tromsø), No. 2
[10] Lawler, E. L., Optimal matroid intersections, (Combinatorial Structures and their Applications. Combinatorial Structures and their Applications, Proc. Calgary International Conference (1970), Gordon and Breach: Gordon and Breach New York), 233-234 · Zbl 0256.05014
[11] Maurer, S., Matroid bases graphs, J. Combinatorial Theory, 14, B, 216-240 (1973) · Zbl 0244.05015
[12] Whitney, H., On the abstract properties of linear dependence, Am. J. Math., 57, 509-533 (1935) · JFM 61.0073.03
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