##
**Zentralblatt MATH**

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

**Zbl.No: ** 686.05029

**Autor: ** Erdös, Paul; Pach, János; Pollack, Richard; Tuza, Zsolt

**Title: ** Radius, diameter, and minimum degree. (In English)

**Source: ** J. Comb. Theory, Ser. B 47, No.1, 73-79 (1989).

**Review: ** The authors prove that the diameter of a connected graph G with n vertices and minimum degree \delta \geq 2 is bounded from above by [3n/(\delta+1)]-1, and that this bound is asymptotically sharp where \delta is fixed and n tends to infinity. They show an analogous result for the radius of G, and also give upper bounds for triangle-free and C^{4}-free connected graphs.

**Reviewer: ** Ch.Schulz

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

05C38 Paths and cycles

**Keywords: ** diameter; minimum degree; radius

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag