Kruskal's theorem for matroids
Dominic J. A. Welsh · Mathematical Proceedings of the Cambridge Philosophical Society · 1968
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.