On the existence of uncountably many matroidal families |
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Authors: | Rüdiger Schmidt |
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Institution: | Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, Hamburg, BRD, Germany |
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Abstract: | A matroidal family is a set ≠ ? of connected finite graphs such that for every finite graph G the edge-sets of those subgraphs of G which are isomorphic to some element of are the circuits of a matroid on the edge-set of G. Simões-Pereira 5] shows the existence of four matroidal families and Andreae 1] shows the existence of a countably infinite series of matroidal families. In this paper we show that there exist uncountably many matroidal families. This is done by using an extension of Andreae's theorem, a construction theorem, and certain properties of regular graphs. Moreover we observe that all matroidal families so far known can be obtained in a unified way. |
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