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**Zentralblatt MATH**

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

**Zbl.No: ** 822.05036

**Autor: ** Erdös, Paul; Füredi, Z.; Gould, R.J.; Gunderson, D.S.

**Title: ** Extremal graphs for intersecting triangles. (In English)

**Source: ** J. Comb. Theory, Ser. B 64, No.1, 89-100 (1995).

**Review: ** A k-fan is a graph with 2k+1 vertices consisting of k 3-cycles having one vertex in common. The authors show that if n \geq 50k^{2} and the graph G_{n} has more than [n^{2}/4]+k^{2}- ck edges, where c equals 1 or 3/2 according as k is odd or even, then G_{n} contains a k-fan; furthermore, the bound for the number of edges is best possible.

**Reviewer: ** J.W.Moon (Edmonton)

**Classif.: ** * 05C35 Extremal problems (graph theory)

05C38 Paths and cycles

**Keywords: ** intersecting triangles; extremal graphs; fan; 3-cycles

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