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X-WR-CALNAME:Discrete Mathematics Group
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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:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260203T163000
DTEND;TZID=Asia/Seoul:20260203T173000
DTSTAMP:20260415T134040
CREATED:20260105T005335Z
LAST-MODIFIED:20260105T054623Z
UID:12035-1770136200-1770139800@dimag.ibs.re.kr
SUMMARY:Xiaofan Yuan (袁晓璠)\, Rainbow structures in edge colored graphs
DESCRIPTION:Let $G = (V\, E)$ be a graph on $n$ vertices\, and let $c : E \to P$\, where $P$ is a set of colors. Let $\delta^c(G) = \min_{v \in V} \{ d^{c}(v) \}$ where $d^c(v)$ is the number of colors on edges incident to a vertex $v$ of $G$. In 2011\, Fujita and Magnant showed that if $G$ is a graph on $n$ vertices that satisfies $\delta^c(G)\geq n/2$\, then for every two vertices $u\, v$ there is a properly-colored $u\,v$-path in $G$. We show that for sufficiently large graphs $G$\, the same bound for $\delta^c(G)$ implies that any two vertices are connected by a rainbow path. We also show sufficient conditions on $\delta^c(G)$ for the existence of a rainbow cycle of length $2k$ in sufficiently large bipartite graphs $G$\, which are tight in many cases. This is joint work with Andrzej Czygrinow.
URL:https://dimag.ibs.re.kr/event/2026-02-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260210T163000
DTEND;TZID=Asia/Seoul:20260210T173000
DTSTAMP:20260415T134040
CREATED:20251120T125949Z
LAST-MODIFIED:20260121T225453Z
UID:11872-1770741000-1770744600@dimag.ibs.re.kr
SUMMARY:Seonghun Park (박성훈)\, Formalizing Flag Algebras in the Lean Theorem Prover
DESCRIPTION:Flag algebras are a mathematical framework introduced by Alexander Razborov in 2007\, which has been used to resolve a wide range of open problems in extremal graph theory in the past twenty years. This framework provides an algebraic setup where one can express relationships between induced subgraph densities symbolically. It also comes with mathematical techniques for systematically deriving such relationships that always hold. Some of these techniques have even been implemented in automatic tools\, such as Flagmatic. In this work\, we formalise flag algebras in Lean\, an interactive theorem prover based on dependent type theory. Lean is computer software that lets us write mathematical definitions and proofs in a computer and check the correctness of written proofs using a computer. By formalizing flag algebras in Lean\, we can ensure that the mathematical foundation of flag algebras does not have any mistakes\, and provide a mathematical guarantee that theorems proved by flag algebras are indeed correct. In this talk\, I will explain flag algebras and our Lean formalization using Mantel’s theorem as a guiding example. In the process\, I will describe the challenges and lessons learned during the formalization. \nThis is a joint work with Jihoon Hyun\, Gyeongwon Jeong\, Sang-il Oum\, and Hongseok Yang.
URL:https://dimag.ibs.re.kr/event/2026-02-10/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260224T163000
DTEND;TZID=Asia/Seoul:20260224T173000
DTSTAMP:20260415T134040
CREATED:20251119T205949Z
LAST-MODIFIED:20260202T004550Z
UID:11865-1771950600-1771954200@dimag.ibs.re.kr
SUMMARY:Marek Sokołowski\, Strongly Polynomial Parallel Work-Depth Tradeoffs for Directed SSSP
DESCRIPTION:In this talk\, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly\, we prove that directed SSSP can be solved within $\widetilde{O}(m+n^{2-\varepsilon})$ work and $\widetilde{O}(n^{1-\varepsilon})$ depth for some positive $\varepsilon>0$. For dense graphs with non-negative real weights\, this yields the first nearly work-efficient strongly polynomial algorithm with sublinear depth. Moreover\, we develop efficient parallel algorithms in the Word RAM model for several variants of SSSP in graphs with exponentially large edge weights. \nThis is a joint work with Adam Karczmarz and Wojciech Nadara.
URL:https://dimag.ibs.re.kr/event/2026-02-24/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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