On a problem of Duke-Erdos-Rodl on cycle-connected subgraphs

Details On a problem of Duke-Erdos-Rodl on cycle-connected subgraphs On a problem of Duke-Erdos-Rodl on cycle-connected subgraphs

2007-06-13

arxiv.org/abs/0706.1920v3

Mathematics

Combinatorics

7 pages

Scientific paper

In this short note, we prove that for \beta < 1/5 every graph G with n vertices and n^{2-\beta} edges contains a subgraph G' with at least cn^{2-2\beta} edges such that every pair of edges in G' lie together on a cycle of length at most 8. Moreover edges in G' which share a vertex lie together on a cycle of length at most 6. This result is best possible up to the constant factor and settles a conjecture of Duke, Erdos, and Rodl.

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