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DTSTART:20190101T000000
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DTSTART;TZID=Asia/Seoul:20190812T110000
DTEND;TZID=Asia/Seoul:20190812T200000
DTSTAMP:20200602T010513
CREATED:20190730T073856Z
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SUMMARY:2019-2 IBS One-Day Conference on Extremal Graph Theory
DESCRIPTION:Invited Speakers\n\nJaehoon Kim (김재훈)\, KAIST\nHong Liu (刘鸿)\, University of Warwick\nAbhishek Methuku\, IBS Discrete Mathematics Group\nPéter Pál Pach\, Budapest University of Technology and Economics\n\nSchedule\nAugust 12\, Monday\n11:00am-12:00pm Jaehoon Kim (김재훈): Tree decompositions of graphs without large bipartite holes \n12:00pm-1:30pm Lunch \n1:30pm-2:30pm Abhishek Methuku: Bipartite Turán problems for ordered graphs \n3:00pm-4:00pm Péter Pál Pach: On some applications of graph theory to number theoretic problems \n4:30pm-5:30pm Hong Liu: Recent advance in Ramsey-Turán theory \n6:00pm-8:00pm Banquet \nAbstract\nJaehoon Kim (김재훈)\, Tree decompositions of graphs without large bipartite holes\nA recent result of Condon\, Kim\, Kühn and Osthus implies that for any $r\geq (\frac{1}{2}+o(1))n$\, an $n$-vertex almost $r$-regular graph $G$ has an approximate decomposition into any collections of $n$-vertex bounded degree trees. In this talk\, we prove that a similar result holds for an almost $\alpha n$-regular graph $G$ with any $\alpha>0$ and a collection of bounded degree trees on at most $(1-o(1))n$ vertices if $G$ does not contain large bipartite holes. This result is sharp in the sense that it is necessary to exclude large bipartite holes and we cannot hope for an approximate decomposition into $n$-vertex trees. This is joint work with Younjin Kim and Hong Liu. \nAbhishek Methuku\, Bipartite Turán problems for ordered graphs\nA zero-one matrix $M$ contains a zero-one matrix $A$ if one can delete rows and columns of $M$\, and turn 1-entries into 0-entries such that the resulting matrix is $A$. The extremal number of $A$\, denoted by $ex(n\,A)$\, is the maximum number of $1$-entries in an $n\times n$ sized matrix $M$ that does not contain $A$. \nA matrix $A$ is column-$t$-partite (or row-$t$-partite)\, if it can be cut along the columns (or rows) into $t$ submatrices such that every row (or column) of these submatrices contains at most one $1$-entry. We prove that if $A$ is column-$t$-partite\, then $\operatorname{ex}(n\,A)