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| KAIST Discrete Math Seminar |
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Title |
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Speaker |
Lee, Choongbum |
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2012-07-04 |
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KAIST |
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File |
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 Abstract : 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. We determine this maximum up to a constant factor and 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 Erdős, Pach, and Pyber from 1987. Joint work with Po-Shen Loh and Benny Sudakov. |
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