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Kruskal's theorem for matroids

Published online by Cambridge University Press:  24 October 2008

D. J. A. Welsh
D. J. A. Welsh
Affiliation:
Merton College, Oxford
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Abstract

Kruskal's theorem for obtaining a minimal (maximal) spanning tree of a graph is shown to be a special case of a more general theorem for matroid spaces in which each element of the matroid has an associated weight. Since any finite subset of a vector space can be regarded as a matroid space this theorem gives an easy method of selecting a linearly independent set of vectors of minimal (maximal) weight.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 3 - 4
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

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