BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:Discrete Mathematics Group X-ORIGINAL-URL:https://dimag.ibs.re.kr X-WR-CALDESC:Events for Discrete Mathematics Group REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:Asia/Seoul BEGIN:STANDARD TZOFFSETFROM:+0900 TZOFFSETTO:+0900 TZNAME:KST DTSTART:20240101T000000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=Asia/Seoul:20251104T163000 DTEND;TZID=Asia/Seoul:20251104T173000 DTSTAMP:20260416T090605 CREATED:20250904T053024Z LAST-MODIFIED:20250904T053024Z UID:11544-1762273800-1762277400@dimag.ibs.re.kr SUMMARY:Ahmed Ghazy and Tim Hartmann\, Continuous Graphs – An Overview and a Coloring Problem DESCRIPTION:We consider a continuous model of graphs\, introduced by Dearing and Francis in 1974\, where each edge of G to be a unit interval\, giving rise to an infinite metric space that contains not only the vertices of G but all points on all edges of G. Several standard graph problems can be defined and studied on continuous graphs\, yielding many surprising algorithmic results and combinatorial connections. \nThe motivation can be exemplified by the well-known Independent Set problem on graphs. Given a graph G\, we want to place k facilities that are pairwise at least a distance 2 edge lengths apart. In some applications\, such as when the underlying graph represents a street network\, it is reasonable to allow placing a facility not only at a crossroad but also somewhere within a street\, that is\, not only at a vertex but also at any point on an edge between two vertices. This motivates the study of the Independent Set problem on continuous graphs. In such a setting\, for example\, the problem corresponds to requiring pairwise distance r=2 for the placed facilities. However\, we may also study the problem where we fix r to any positive integer\, rational\, or even irrational number. Other problems studied in the continuous model include Dominating Set\, TSP\, and Coloring. \nIn the first part of this talk\, we will give a general overview of research on continuous graphs and computational problems in this setting. \nIn the second part\, we explore\, as part of recent work\, a coloring problem on continuous graphs akin to the well-known Hadwiger-Nelson Problem. \nBased on joint work with Fabian Frei\, Florian Hörsch\, Tom Janßen\, Stefan Lendl\, Dániel Marx\, Prahlad Narasimhan\, and Gerhard Woeginger. URL:https://dimag.ibs.re.kr/event/2025-11-04/ LOCATION:Room B332\, IBS (기초과학연구원) CATEGORIES:Discrete Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=Asia/Seoul:20251111T163000 DTEND;TZID=Asia/Seoul:20251111T173000 DTSTAMP:20260416T090605 CREATED:20250923T135954Z LAST-MODIFIED:20250923T135954Z UID:11635-1762878600-1762882200@dimag.ibs.re.kr SUMMARY:Simón Piga\, Turán problem in hypergraphs with quasirandom links DESCRIPTION:Given a $k$-uniform hypergraph $F$\, its Turán density $\pi(F)$ is the infimum over all $d\in [0\,1]$ such that any $n$-vertex $k$-uniform hypergraph $H$ with at least $d\binom{n}{k}+o(n^k)$ edges contains a copy of $F$. While Turán densities are generally well understood for graphs ($k=2$)\, the problem becomes notoriously difficult for $k\geq 3$\, even for small hypergraphs. \nWe study two well-known variants of this Turán problem for hypergraphs: first\, under minimum codegree conditions and\, second\, with a quasirandom edge distribution. Each variant defines a distinct extremal parameter\, generalising the classical Turán density. Here we present recent results in both settings\, with a particular emphasis on the case of hypergraphs where every link is itself quasirandom. Our results include exact solutions for key hypergraphs and general results about the behaviour of the Turán density functions. URL:https://dimag.ibs.re.kr/event/2025-11-11/ LOCATION:Room B332\, IBS (기초과학연구원) CATEGORIES:Discrete Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=Asia/Seoul:20251118T163000 DTEND;TZID=Asia/Seoul:20251118T173000 DTSTAMP:20260416T090605 CREATED:20251016T022138Z LAST-MODIFIED:20251104T135407Z UID:11731-1763483400-1763487000@dimag.ibs.re.kr SUMMARY:Fedor Noskov\, Polynomial dependencies in hypergraph Turan-type problems DESCRIPTION:Consider a general Turan-type problem on hypergraphs. Let $\mathcal{F}$ be a family of $k$-subsets of $[n]$ that does not contain sets $F_1\, \ldots\, F_s$ satisfying some property $P$. We show that if $P$ is low-dimensional in some sense (e.g.\, is defined by intersections of bounded size) then\, under polynomial dependencies between $n\, k$ and the parameters of $P$\, one can reduce the problem of maximizing the size of the family $|\mathcal{F}|$ to a finite extremal set theory problem independent of $n$ and $k$. We show that our technique implies new bounds in a number of Turan-type problems including the Erdős-Sós forbidden intersection problem\, the Duke-Erdős forbidden sunflower problem\, forbidden $(t\, d)$-simplex problem and the forbidden hypergraph problem. Furthermore\, we also briefly discuss the connection between the aforementioned reduction and the measure boosting argument based on the action of a certain semigroup on the Boolean cube.  This connection turns out to be fruitful when extending extremal set theory problems to domains different from $\binom{[n]}{k}$. \nJoint work with Liza Iarovikova\, Andrey Kupavskii\, Georgy Sokolov and Nikolai Terekhov URL:https://dimag.ibs.re.kr/event/2025-11-18/ LOCATION:Room B332\, IBS (기초과학연구원) CATEGORIES:Discrete Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=Asia/Seoul:20251125T163000 DTEND;TZID=Asia/Seoul:20251125T173000 DTSTAMP:20260416T090605 CREATED:20250929T123857Z LAST-MODIFIED:20251104T141401Z UID:11664-1764088200-1764091800@dimag.ibs.re.kr SUMMARY:Péter Pál Pach\, Product representation of perfect cubes DESCRIPTION:Let $F_{k\,d}(n)$ be the maximal size of a set ${A}\subseteq [n]$ such that the equation \[a_1a_2\cdots a_k=x^d\, \; a_1