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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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DTSTART:20180101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20190103T160000
DTEND;TZID=Asia/Seoul:20190103T170000
DTSTAMP:20260423T192124
CREATED:20181224T085518Z
LAST-MODIFIED:20240707T090650Z
UID:305-1546531200-1546534800@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, Sidorenko’s conjecture for blow-ups
DESCRIPTION:A celebrated conjecture of Sidorenko and Erdős–Simonovits states that\, for all bipartite graphs H\, quasirandom graphs contain asymptotically the minimum number of copies of H taken over all graphs with the same order and edge density. This conjecture has attracted considerable interest over the last decade and is now known to hold for a broad range of bipartite graphs\, with the overall trend saying that a graph satisfies the conjecture if it can be built from simple building blocks such as trees in a certain recursive fashion. \nOur contribution here\, which goes beyond this paradigm\, is to show that the conjecture holds for any bipartite graph H with bipartition A∪B where the number of vertices in B of degree k satisfies a certain divisibility condition for each k. As a corollary\, we have that for every bipartite graph H with bipartition A∪B\, there is a positive integer p such that the blow-up HAp formed by taking p vertex-disjoint copies of H and gluing all copies of A along corresponding vertices satisfies the conjecture. Joint work with David Conlon.
URL:https://dimag.ibs.re.kr/event/2019-01-03/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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