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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 242.05113

**Autor: ** Erdös, Paul; Hajnal, András; Milner, E.C.

**Title: ** Simple one-point extensions of tournaments. (In English)

**Source: ** Mathematika, Lond. 19, 57-62 (1972).

**Review: ** A tournament T consists of a set of points on which is defined a complete, anti-symmetric, irreflexive binary relation \rho. A tournament T is simple if it is impossible to define a non-trivial equivalence relation on the points of T with the property that if x \rho y then x' \rho y' for all pairs of points x' and y' that are equivlent to x and y, respectively. If T is a subtournament of T' and |T' - T| = k then T' is a k-point extension of T. The authors prove that s (finite or infinite) tournament T has a simple 1-point extension except when T is a 3-cycle of a non-trivial finite transitive tournament with an odd number of points.

**Reviewer: ** J.W.Moon

**Classif.: ** * 05C20 Directed graphs (digraphs)

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