Abstract
By generalizing matroid axiomatics we provide a framework in which independence systems may be classified. The concept is applied to independence systems arising from well-known combinatorial optimization problems such ask-matroid-intersection-, matchoid-, vertex packingor travelling salesman-problems.
Zusammenfassung
Durch Verallgemeinerung von Matroid-Axiomen entwickeln wir ein Schema, in dem Unabhängigkeitssysteme klassifiziert werden können. Der Ansatz wird auf solche Unabhängigkeitssysteme angewandt, die durch wohlbekannte, kombinatorische Optimierungsprobleme gegeben sind wie etwak-Matroid-Schnitt-, Matchoid-, Stabile Mengen- oder Rundreise-Probleme.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Giles, R.: Optimum Matching Forests I. Math. Programming22, 1982, 1–11.
Jenkyns, T.A.: Matchoids: A Generalization of Matchings and Matroids. Thesis, University of Waterloo, 1974.
Lawler, E.L.: Combinatorial Optimization: Networks and Matroids. New York 1976.
Lovász, L.: The Matroid Parity Problem. University of Waterloo, 1979.
Minty, G.J.: On Maximal independent Sets of Vertices in Claw-Free Graphs. Journal of Comb. Theory (B)28, 1980, 284–304.
Mirsky, L.: Transversal Theory. New York 1971.
Sakarovitch, M.: Deux ou Trois Choses que Je Sais des Bitroides. Rapport de Recherche No. 55, IMAG, Université de Grenoble, November 1976.
Sbihi, N.: Algorithme de Recherche d'un Stable de Cardinalité Maximum dans un Graphe sans Etoile. Discrete Mathematics29, 1980, 53–76.
Welsh, D.: Matroid Theory. New York 1976.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Euler, R. On a classification of independence systems. Zeitschrift für Operations Research 27, 123–136 (1983). https://doi.org/10.1007/BF01916906
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01916906