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PRODID:-//Discrete Mathematics Group - ECPv6.16.2//NONSGML v1.0//EN
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X-WR-CALNAME:Discrete Mathematics Group
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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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
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DTSTART:20200101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211005T163000
DTEND;TZID=Asia/Seoul:20211005T173000
DTSTAMP:20260525T100312
CREATED:20211005T073000Z
LAST-MODIFIED:20240707T080940Z
UID:4503-1633451400-1633455000@dimag.ibs.re.kr
SUMMARY:Eunjin Oh (오은진)\, Feedback Vertex Set on Geometric Intersection Graphs
DESCRIPTION:I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k\, if it exists\, which runs in time $2^{O(\sqrt{k})}(n + m)$\, where $n$ and $m$ denote the numbers of vertices and edges\, respectively. This improves the $2^{O(\sqrt{k}\log k)}(n + m)$-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017].
URL:https://dimag.ibs.re.kr/event/2021-10-05/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211012T163000
DTEND;TZID=Asia/Seoul:20211012T173000
DTSTAMP:20260525T100312
CREATED:20211012T073000Z
LAST-MODIFIED:20240707T080915Z
UID:4374-1634056200-1634059800@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, Majority dynamics on sparse random graphs
DESCRIPTION:Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini\, Chan\, O’Donnell\, Tamuz and Tan conjectured that\, in the Erdős-Rényi random graph $G(n\,p)$\, the random initial $\pm 1$-assignment converges to a $99\%$-agreement with high probability whenever $p=\omega(1/n)$. \nThis conjecture was first confirmed for $p\geq\lambda n^{-1/2}$ for a large constant $\lambda$ by Fountoulakis\, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin\, it was unknown whether the conjecture holds for $p< \lambda n^{-1/2}$. We break this $\Omega(n^{-1/2})$-barrier by proving the conjecture for sparser random graphs $G(n\,p)$\, where $\lambda’ n^{-3/5}\log n \leq p \leq \lambda n^{-1/2}$ with a large constant $\lambda’>0$. \nJoint work with Debsoumya Chakraborti\, Jeong Han Kim and Tuan Tran.
URL:https://dimag.ibs.re.kr/event/2021-10-12/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211026T163000
DTEND;TZID=Asia/Seoul:20211026T173000
DTSTAMP:20260525T100312
CREATED:20211026T073000Z
LAST-MODIFIED:20240707T080901Z
UID:4709-1635265800-1635269400@dimag.ibs.re.kr
SUMMARY:Donggyu Kim (김동규)\, 𝝘-graphic delta-matroids and their applications
DESCRIPTION:Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define a $\Gamma$-graphic delta-matroid for an abelian group $\Gamma$\, which generalizes a graphic delta-matroid. \nFor an abelian group $\Gamma$\, a $\Gamma$-labelled graph is a graph whose vertices are labelled by elements of $\Gamma$. We prove that a certain collection of edge sets of a $\Gamma$-labelled graph forms a delta-matroid\, which we call a $\Gamma$-graphic delta-matroid\, and provide a polynomial-time algorithm to solve the separation problem\, which allows us to apply the symmetric greedy algorithm of Bouchet (1987) to find a maximum weight feasible set in such a delta-matroid. We also prove that a $\Gamma$-graphic delta-matroid is a graphic delta-matroid if and only if it is even. We prove that every $\mathbb{Z}_p^k$-graphic delta matroid is represented by some symmetric matrix over a field of characteristic of order $p^k$\, and if every $\Gamma$-graphic delta-matroid is representable over a finite field $\mathbb{F}$\, then $\Gamma$ is isomorphic to $\mathbb{Z}_p^k$ and $\mathbb{F}$ is a field of order $p^\ell$ for some prime $p$ and positive integers $k$ and $\ell$. \nThis is joint work with Duksang Lee and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-10-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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