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**Zentralblatt MATH**

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

**Zbl.No: ** 129.39904

**Autor: ** Erdös, Pál; Pósa, L.

**Title: ** On independent circuits contained in a graph (In English)

**Source: ** Can. J. Math. 17, 347-352 (1965).

**Review: ** Let r(k) denote the least integer r such that if G is any graph containing a maximum of k node-disjoint circuits then there exists a set of r nodes of G such that every circuit of G passes through at least one of these nodes. Bollbás (unpublished) has shown that r(1) = 3. (The complete 5-graph shows that r(1) \geq 3.) In the present paper it is shown that there exist absolute constants c_{1} and c_{2} such that c_{1}k log k < r(k) < c_{2}k log k.

**Reviewer: ** J.W.Moon

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

**Index Words: ** topology

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