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**Zentralblatt MATH**

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

**Zbl.No: ** 099.39401

**Autor: ** Erdös, Pál

**Title: ** On a theorem of Rademacher-Turán. (In English)

**Source: ** Ill. J. Math. 6, 122-127 (1962).

**Review: ** Non-directed finite graphs without loops and parallel edges are considered. The main result is: there exists a positive constant c_{1} such that, if t < ^{1}/_{2} c_{1}n, any graph having n vertices and **[** ^{1}/_{4} n^{2} **]**+t edges contains at least t**[** ^{1}/_{2} n **]** triangles. One of the lemma states: if a graph has n vertices and **[** ^{1}/_{4} (n-1)^{2} **]**+2 edges, then either it is even or it contains a triangle. – [Reviewer's note: – 3 must be added to the left-hand side of the formula (1) on p. 124. This correction does not touch the validity of the further estimations.]

**Reviewer: ** A.Ádám

**Classif.: ** * 05C38 Paths and cycles

**Index Words: ** topology

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag