Self-Similarity of Graphs
نویسندگان
چکیده
An old problem raised independently by Jacobson and Schönheim 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 logm) edges for some absolute constant c, and find graphs where this estimate is off only by a multiplicative constant. Our results improve bounds of Erdős, Pach, and Pyber from 1987.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 27 شماره
صفحات -
تاریخ انتشار 2013