Edmonds: partitioning a matroid into independent sets

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Jack Edmonds, "Minimum partition of a matroid into independent subsets," Journal of Research of the National Bureau of Standards, Section B 69B (1965), 67--72.

Edmonds proves the matroid partition criterion: the ground set of a matroid, which the paper's definition makes finite, can be partitioned into $k$ independent sets exactly when every subset $A$ has rank at least $|A|/k$ (equivalently $|A|\le k r(A)$). This is the exact matroid analogue of the implication asked about in E0774.