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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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DTSTART:20180101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20190812T110000
DTEND;TZID=Asia/Seoul:20190812T200000
DTSTAMP:20260424T081019
CREATED:20190730T073856Z
LAST-MODIFIED:20240707T090147Z
UID:1201-1565607600-1565640000@dimag.ibs.re.kr
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 $\operatorname{ex}(n\,A)<n^{2-\frac{1}{t}+\frac{1}{2t^{2}}+o(1)}$\, and if $A$ is both column- and row-$t$-partite\, then $\operatorname{ex}(n\,A)<n^{2-\frac{1}{t}+o(1)}$\, and this bound is close to being optimal. Our proof introduces a new density-increment-type argument which is combined with the celebrated dependent random choice method. \nResults about the extremal numbers of zero-one matrices translate into results about the Turán numbers of bipartite ordered graphs. In particular\, a zero-one matrix with at most $t$ 1-entries in each row corresponds to an ordered graph with maximum degree $t$ in one of its vertex classes. The aim of this talk is to establish general results about the extremal numbers of ordered graphs. Our results are partially motivated by a well known result of Füredi (1991) and Alon\, Krivelevich\, Sudakov (2003) stating that if $H$ is a bipartite graph with maximum degree $t$ in one of the vertex classes\, then $\operatorname{ex}(n\,H)=O(n^{2-\frac{1}{t}})$. This is joint work with Tomon. \nPéter Pál Pach\, On some applications of graph theory to number theoretic problems\nHow large can a set of integers be\, if the equation $a_1a_2\dots a_h=b_1b_2\dots b_h$ has no solution consisting of distinct elements of this set? How large can a set of integers be\, if none of them divides the product of $h$ others? How small can a multiplicative basis for $\{1\, 2\, \dots\, n\}$ be? The first question is about a generalization of the multiplicative Sidon sets\, the second one is of the primitive sets\, while the third one is the multiplicative version of the well-studied analogue problem for additive bases. \nIn answering the above mentioned questions graph theory plays an important role and in most of our results not only the asymptotics are found\, but very tight bounds are obtained for the error terms\, as well. We will also discuss the counting version of these questions. \nHong Liu\, Recent advance in Ramsey-Turán theory\nWe will talk about Ramsey-Turán theory and some recent development. More specifically\, we will talk about graphs with $\alpha_r(G)=o(n)$\, where $\alpha_r(G)$ is the largest size subset with no $K_r$. Two major open problems in this area from the 80s ask: (1) whether Bollobas-Erdos graph can be generalised to densities other than $1/2$; (2) whether the asymptotic extremal structure for $\alpha_r(G)$ resembles that of $\alpha_2(G)$. We settle the first conjecture by constructing Bollobas-Erdos type graph with density $a$ for arbitrary rational number $a\le 1/2$; and refute the second conjecture by witnessing asymptotic extremal structures that are drastically different from the $\alpha_2(G)$ problem via a ”Mobius product” construction. \nJoint work with Christian Reiher\, Maryam Sharifzadeh\, and Katherine Staden.
URL:https://dimag.ibs.re.kr/event/2019-08-12/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20190813
DTEND;VALUE=DATE:20190816
DTSTAMP:20260424T081019
CREATED:20190410T011602Z
LAST-MODIFIED:20240707T090140Z
UID:748-1565654400-1565913599@dimag.ibs.re.kr
SUMMARY:2019 Combinatorics Workshop
DESCRIPTION:The annual conference on Combinatorics Workshop (조합론 학술대회) began in 2004 by the Yonsei University BK21 Research Group. This year it will take place in Songdo\, Incheon\, August 13-15\, 2019. \n\n\n\n\n\n\n\n\n\nDue to the capacity (50 persons) of the place\, we are able to limit your registration. In principle\, registration is on a first-come\, first-served basis. \n\n\n\n\n\n\n\n\n\n\nTitle 2019 Combinatorics Workshop (2019 조합론 학술대회)\nDate August 13-15 (Tue-Thu)\, 2019\nVenue Hotel Skypark\, Songdo\, Incheon\nWeb https://cw2019.combinatorics.kr\n\nWe are going to \n\ngive six 50-minute talks and ten 25-minute talks in Korean.\ndistribute the program and abstracts of CW2019.\nprovide for the accommodations for all participants.\nprovide for six meals (two breakfasts\, two luncheons\, one dinner\, and one banquet) for all participants.\n\nPlenary Speaker\n\nMihyun Kang\, Graz University of Technology\n\nKeynote Speakers\n\nJaehoon Kim\, KAIST\nSeung Jin Lee\, Seoul National University\nMeesue Yoo\, Dankook University\n\nInvited Speakers\n\nEun-Kyung Cho\, Hankuk University of Foreign Studies\nSoogang Eoh\, Seoul National University\nJiSun Huh\, Sungkyunkwan University\nJihyeug Jang\, Sungkyunkwan University\nDong Yeap Kang\, KAIST and IBS Discrete Mathematics Group\nMin Jeong Kang\, Incheon National University\nDabeen Lee\, IBS Discrete Mathematics Group\nKang-Ju Lee\, Seoul National University\nMyeonghwan Lee\, Incheon National University\nJihye Park\, Yeungnam University\nSun-mi Yun\, Sungkyunkwan University\n\nOrganizing Committee\n\nO-joung Kwon\, Incheon National University and IBS Discrete Mathematics Group\nSuil O\, SUNY Korea\nSang-il Oum\, IBS Discrete Mathematics Group and KAIST\nHeesung Shin\, Inha University\n\nAdvisory Committee\n\nCommittee of Discrete Mathematics\, The Korean Mathematical Society (Chair: Seog-Jin Kim\, Konkuk University)\n\nSponsors\n\nIBS Discrete Mathematics Group\nNRF (National Research Foundation of Korea)
URL:https://dimag.ibs.re.kr/event/2019-combinatorics-workshop/
LOCATION:Hotel Skypark\, Songdo\, Incheon\, Korea (송도 스카이파크호텔)
CATEGORIES:Workshops and Conferences
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