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Quasi-random tournaments. (English) Zbl 0728.05025
The authors consider certain properties that tournaments \(T_ n\) might possess; a typical such property might be that the value of some parameter defined on \(T_ n\) lies in a certain interval that, roughly speaking, is not too wide. They show that a number of such properties are equivalent in the sense that if \(T_ n\) possesses any one of them it possesses all of them.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C80 Random graphs (graph-theoretic aspects)
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[1] Alon, Discrete Math. 75 pp 23– (1989)
[2] Random Graphs. Academic Press, New York (1985).
[3] Bollobás, Eur. J. Combinat. 2 pp 13– (1981) · Zbl 0471.05037
[4] Burgess, Proc. London Math. Soc. 12 pp 179– (1962)
[5] Chung, Rand. Struct. Algor. 1 pp 363– (1990)
[6] Chung, Rand. Struct. Algor. 1 pp 105– (1990)
[7] and , On graphs not containing prescribed induced subgraphs. To appear. · Zbl 0743.05028
[8] and , Maximum cuts and quasi-random graphs. To appear.
[9] and , Quasi-random graphs. Combinatorica 9 (1989) 345–362. · Zbl 0715.05057
[10] Erdös, Math. Gazette 47 pp 220– (1963)
[11] Erdös, Discrete Math. 75 pp 145– (1989)
[12] Erdös, Networks 1 pp 379– (1972)
[13] and , Probabilistic Methods in Combinatorics. Akadémiai Kiadó, Budapest (1974).
[14] Frankl, J. Combinat. Theory B 44 pp 317– (1988)
[15] Graham, Can. Math. Bull. 14 pp 45– (1971) · Zbl 0209.55804
[16] Topics on Tournaments. Holt, New York (1968). · Zbl 0191.22701
[17] and , Tournaments. Selected Topics in Graph Theory. Academic Press, New York (1978) chap. 7.
[18] and , Quasi-random graphs with tolerance . Unpublished manuscript.
[19] Szekeres, Math. Gazette 49 pp 290– (1965)
[20] Thomason, Ann. Discrete Math. 33 pp 307– (1987)
[21] Random graphs, strongly regular graphs and pseudorandom graphs. Surveys in Combinatorics 1987, LMS Lecture Notes Series 123. Cambridge University Press, Cambridge (1987) 173–196.
[22] Weil, Actualités Sci. Ind. 1041 (1948)
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