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Landau’s and Rado’s theorems and partial tournaments. (English) Zbl 1159.05014
Summary: Using Rado’s theorem for the existence of an independent transversal of family of subsets of a set on which a matroid is defined, we give a proof of Landau’s theorem for the existence of a tournament with a prescribed degree sequence. A similar approach is used to determine when a partial tournament can be extended to a tournament with a prescribed degree sequence.

MSC:
05C07 Vertex degrees
05C20 Directed graphs (digraphs), tournaments
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05B35 Combinatorial aspects of matroids and geometric lattices
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