##
**Zentralblatt MATH**

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

**Zbl.No: ** 129.39905

**Autor: ** Erdös, Pál

**Title: ** On extremal problems of graphs and generalized graphs (In English)

**Source: ** Isr. J. Math. 2, 183-190 (1964).

**Review: ** An r-graph G consists of a set V(G) of elements called vertices of G and a set E(G) whose elements (called edges of G) are subsets of V(G) with cardinal number r. (Thus a 2-graph is a graph in the usual sense.) The paper deals with the following problem: given positive integers n,r,l, estimate the smallest value of f such that, for every r-graph G with n vertices and f edges, V(G) has r disjoint subsets S_{1},...,S_{r} of cardinal number l such that **{**x_{1},...,x_{r}**}** in E(G) whenever x_{1} in S_{1},...,x_{r} in S_{r}. Some related matters are also briefly discussed and some interesting results and unsolved problems in this area are mentioned.

**Reviewer: ** C.St.J.A.Nash-Williams

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

**Index Words: ** topology

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag