Abstract
The first application of matroids in transversal theory goes back to the early forties and since then they have played the essential role in this area. As a matter of fact, there are two fundamental results concerning both transversals and matroids. In [9] Rado established a necessary and sufficient condition for a finite family of sets to possess a transversal which is independent in a given matroid. The second result, stated by Edmonds and Fulkerson [3], says that the partial transversals of a finite family of sets form a matroid. The two theorems lie at the very heart of transversal theory and therefore there are many variations and generalizations of them. A comprehensive survey of this field is in [7], for later ones see e.g. [10]. Yet, the generalizations of these classical results seem to go in different directions. In this paper it is shown that by means of k-transversals, introduced by Asratian [1] and originally called compatible transversals, it is possible to obtain “parallel” generalization of them.
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References
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© 1990 Physica-Verlag Heidelberg
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Horák, P. (1990). Transversals and Matroids. In: Bodendiek, R., Henn, R. (eds) Topics in Combinatorics and Graph Theory. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46908-4_43
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DOI: https://doi.org/10.1007/978-3-642-46908-4_43
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-642-46910-7
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