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Landau’s theorem revisited. (English) Zbl 0946.05043
Two new elementary proofs are given of Landau’s theorem on necessary and sufficient conditions for a sequence of integers to be a score sequence for some tournament. The first one starts from the transitive tournament that is than modified step by step until a tournament with the desired score sequence is reached. The second one starts from the score sequence itself modifying it step by step, working its way “upwards” to the transitive tournament. Once this is reached, reversing the process gives a construction for a tournament having the desired score sequence.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 11B75 Other combinatorial number theory
##### Keywords:
Landau’s theorem; score sequence; tournament