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**Zentralblatt MATH**

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

**Zbl.No: ** 559.05038

**Autor: ** Duke, Richard; Erdös, Paul; Rödl, Vojtech

**Title: ** More results on subgraphs with many short cycles. (In English)

**Source: ** Combinatorics, graph theory and computing, Proc. 15th Southeast. Conf., La. State Univ. 1984, Congr. Numerantium 43, 295-300 (1984).

**Review: ** [For the entire collection see Zbl 547.00011.]

The authors show that for sufficiently large n every graph of order n and size n^{2-3\epsilon} contains a subgraph of order m and size cn^{2-\epsilon}, where c does not depend on m, n or \epsilon, in which every two edges are on a cycle of length at most 6, and that apart from the value of c this result is best possible, i.e., 3 cannot be replaced by any smaller value.

**Reviewer: ** L.Lesniak

**Classif.: ** * 05C38 Paths and cycles

**Keywords: ** cycle

**Citations: ** Zbl 547.00011

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