## 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 Bollbás (unpublished) has shown that r(1) = 3.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 c1 and c2 such that c1k log k < r(k) < c2k log k.
Reviewer:  J.W.Moon
Classif.:  * 05C35 Extremal problems (graph theory)
Index Words:  topology

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