Date of Original Version

2-2013

Type

Article

Rights Management

© 2013, Society for Industrial and Applied Mathematics

Abstract or Description

An old problem raised independently by Jacobson and Sch¨onheim asks to determine the maximum s for which every graph with m edges contains a pair of edge-disjoint isomorphic subgraphs with s edges. In this paper we determine this maximum up to a constant factor. We show that every m-edge graph contains a pair of edge-disjoint isomorphic subgraphs with at least c(m log m) 2/3 edges for some absolute constant c, and find graphs where this estimate is off only by a multiplicative constant. Our results improve bounds of Erdos, Pach, and Pyber from 1987.

DOI

10.1137/120861436

Included in

Mathematics Commons

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Published In

SIAM Journal on Discrete Mathematics, 27, 2, 959-972.