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**Zentralblatt MATH**

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

**Zbl.No: ** 214.02703

**Autor: ** Erdös, Paul; Hajnal, András

**Title: ** Some results and problems on certain polarized partitions (In English)

**Source: ** Acta Math. Acad. Sci. Hung. 21, 369-392 (1970).

**Review: ** Several rather technical results are proved on polarised partitions and also many perhaps unexpected counterexamples are found. It is impossible to summarize the results, thus we just state one counterexample. Assume the generalized continuum hypothesis than in a set of power \alpha^+ we can define \alpha^+ forests not containing infinite paths so that given \alpha^+ edges all but less than \alpha of the forests have an edge among the given edges (Theorem 4.1). Several unsolved problems are stated. See further the paper of *A.Hajnal* [Fundam. Math. 69, 39-53 (1970; Zbl 208.01601)].

**Classif.: ** * 05A18 Partitions of sets

00A07 Problem books

**Citations: ** Zbl 208.016

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