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Tournaments and semicomplete digraphs. (English) Zbl 1407.05102
Bang-Jensen, Jørgen (ed.) et al., Classes of directed graphs. Cham: Springer. Springer Monogr. Math., 35-124 (2018).
Summary: The class of tournaments is by far the most well-studied class of digraphs with many deep and important results. Since J. W. Moon’s pioneering book [Topics on tournaments. New York etc: Holt, Rinehart and Winston (1968; Zbl 0191.22701)], the study of tournaments and their properties has flourished and research on tournaments is still a very active area. Often this research deals with the superclass of semicomplete digraphs which are digraphs with no pair of non-adjacent vertices (that is, contrary to tournaments, we allow directed cycles of length 2). In this chapter we cover a very broad range of results on tournaments and semicomplete digraphs from classical to very recent ones. In order to stimulate further research, we not only list a number of open problems, but also give a number of proofs which illustrate the diversity of proof techniques that have been applied. These range from elementary to quite advanced.
For the entire collection see [Zbl 1398.05002].

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
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