BEGIN:VCALENDAR
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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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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:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220104T163000
DTEND;TZID=Asia/Seoul:20220104T173000
DTSTAMP:20260423T223141
CREATED:20211210T230406Z
LAST-MODIFIED:20240707T080549Z
UID:5000-1641313800-1641317400@dimag.ibs.re.kr
SUMMARY:Seunghun Lee (이승훈)\, Transversals and colorings of simplicial spheres
DESCRIPTION:Motivated from the surrounding property of a point set in $\mathbb{R}^d$ introduced by Holmsen\, Pach and Tverberg\, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum transversal ratio of simplicial $d$-spheres\, we provide two infinite constructions. The first construction gives infinitely many $(d+1)$-dimensional simplicial polytopes with the transversal ratio exactly $\frac{2}{d+2}$ for every $d\geq 2$. In the case of $d=2$\, this meets the previously well-known upper bound $1/2$ tightly. The second gives infinitely many simplicial 3-spheres with the transversal ratio greater than $1/2$. This was unexpected from what was previously known about the surrounding property. Moreover\, we show that\, for $d\geq 3$\, the facet hypergraph $\mathcal{F}(\mathbf{P})$ of a $(d+1)$-dimensional simplicial polytope $\mathbf{P}$ has the chromatic number $\chi(\mathcal{F}(\mathbf{P})) \in O(n^{\frac{\lceil d/2\rceil-1}{d}})$\, where $n$ is the number of vertices of $\mathbf{P}$. This slightly improves the upper bound previously obtained by Heise\, Panagiotou\, Pikhurko\, and Taraz. This is a joint work with Joseph Briggs and Michael Gene Dobbins.
URL:https://dimag.ibs.re.kr/event/2022-01-04/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220111T163000
DTEND;TZID=Asia/Seoul:20220111T173000
DTSTAMP:20260423T223141
CREATED:20220111T073000Z
LAST-MODIFIED:20240707T080542Z
UID:5083-1641918600-1641922200@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, Some recent results on geometric transversals
DESCRIPTION:A geometric transversal to a family of convex sets in $\mathbb R^d$ is an affine flat that intersects the members of the family. While there exists a far-reaching theory concerning 0-dimensional transversals (intersection patterns of convex sets)\, much less is known when it comes to higher-dimensional transversals. In this talk\, I will present some new and old results and problems regarding geometric transversals\, based on joint work with Otfried Cheong and Xavier Goaoc.
URL:https://dimag.ibs.re.kr/event/2022-01-11/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220113T163000
DTEND;TZID=Asia/Seoul:20220113T173000
DTSTAMP:20260423T223141
CREATED:20220113T073000Z
LAST-MODIFIED:20240707T080528Z
UID:5009-1642091400-1642095000@dimag.ibs.re.kr
SUMMARY:Ron Aharoni\, A strong version of the Caccetta-Haggkvist conjecture
DESCRIPTION:The Caccetta-Haggkvist conjecture\, one of the best known in graph theory\, is that in a digraph with $n$ vertices in which all outdegrees are at least $n/k$ there is a directed cycle of length at most $k$. This is known for  large values of $k$\, relatively to n\, and asymptotically for n large. A few years ago I offered a generalization: given sets $F_1$\, $\ldots$\, $F_n$ of sets of undirected edges\, each of size at least $n/k$\, there exists a rainbow undirected cycle of length  at most $k$. The directed version is obtained by taking as $F_i$ the set of edges going out of the vertex $v_i$ ($i \le n$)\, with the directions removed. I will tell about recent results on this conjecture\, obtained together with He Guo\, with Beger\, Chudnovsky and Zerbib\, and with DeVos and Holzman.
URL:https://dimag.ibs.re.kr/event/2022-01-13/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220118T163000
DTEND;TZID=Asia/Seoul:20220118T173000
DTSTAMP:20260423T223141
CREATED:20220118T073000Z
LAST-MODIFIED:20240707T080518Z
UID:5105-1642523400-1642527000@dimag.ibs.re.kr
SUMMARY:Jaehyeon Seo (서재현)\, A rainbow Turán problem for color-critical graphs
DESCRIPTION:For given $k$ graphs $G_1\,\dots\, G_k$ over a common vertex set of size $n$\, what conditions on $G_i$ ensures a ‘colorful’ copy of $H$\, i.e. a copy of $H$ containing at most one edge from each $G_i$? \nKeevash\, Saks\, Sudakov\, and Verstraëte defined $\operatorname{ex}_k(n\,H)$ to be the maximum total number of edges of the graphs $G_1\,\dots\, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n\,K_r)$ for large $n$ by showing that\, depending on the value of $k$\, one of the two natural constructions is always the extremal construction. Moreover\, they conjectured the same holds for every color-critical graphs and proved it for $3$-color-critical graphs. \nWe prove their conjecture for $4$-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover\, we show that for every non-color-critical non-bipartite graphs\, none of the two natural constructions is extremal for certain values of $k$. This is a joint work with Debsoumya Chakraborti\, Jaehoon Kim\, Hyunwoo Lee\, and Hong Liu.
URL:https://dimag.ibs.re.kr/event/2022-01-18/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220120T163000
DTEND;TZID=Asia/Seoul:20220120T173000
DTSTAMP:20260423T223141
CREATED:20220120T073000Z
LAST-MODIFIED:20240705T175100Z
UID:4564-1642696200-1642699800@dimag.ibs.re.kr
SUMMARY:Ken-ichi Kawarabayashi (河原林 健一)\, Toward Directed Graph Minor Theory
DESCRIPTION:Graph Minor project by Robertson and Seymour is perhaps the deepest theory in Graph Theory. It gives a deep structural characterization of graphs without any graph $H$ as a minor. It also gives many exciting algorithmic consequences. \nIn this work\, I would like to talk about our attempt to extend Graph minor project to directed graphs. Topics include \n1. The directed grid theorem\n2. The directed flat wall theorem\n3. Tangle tree decomposition\n4. Variant of the directed disjoint paths problems\n5. Toward the structure (and decomposition) theorem for H-minor-free digraphs. \nJoint work with Stephan Kreutzer\, O-joung Kwon\, Archontia Giannopoulou.
URL:https://dimag.ibs.re.kr/event/2022-01-20/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220125T163000
DTEND;TZID=Asia/Seoul:20220125T173000
DTSTAMP:20260423T223141
CREATED:20220125T073000Z
LAST-MODIFIED:20240705T175100Z
UID:5129-1643128200-1643131800@dimag.ibs.re.kr
SUMMARY:O-joung Kwon (권오정)\, Reduced bandwidth: a qualitative strengthening of twin-width in minor-closed classes (and beyond)
DESCRIPTION:In a reduction sequence of a graph\, vertices are successively identified until the graph has one vertex. At each step\, when identifying $u$ and $v$\, each edge incident to exactly one of $u$ and $v$ is coloured red. Bonnet\, Kim\, Thomassé\, and Watrigant [FOCS 2020] defined the twin-width of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has maximum degree at most $k$. For any graph parameter $f$\, we define the reduced-$f$ of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has $f$ at most $k$. Our focus is on graph classes with bounded reduced-bandwidth\, which implies and is stronger than bounded twin-width (reduced-maximum-degree). \nWe show that every proper minor-closed class has bounded reduced-bandwidth\, which is qualitatively stronger than a result of Bonnet et al. for bounded twin-width. In many instances\, we also make quantitative improvements. For example\, all previous upper bounds on the twin-width of planar graphs were at least $2^{1000}$. We show that planar graphs have reduced-bandwidth at most $466$ and twin-width at most $583$; moreover\, the witnessing reduction sequence can be constructed in polynomial time. We show that $d$-powers of graphs in a proper minor-closed class have bounded reduced-bandwidth (irrespective of the degree of the vertices). \nThis is joint work with Édouard bonnet and David Wood.
URL:https://dimag.ibs.re.kr/event/2022-01-25/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220127T163000
DTEND;TZID=Asia/Seoul:20220127T173000
DTSTAMP:20260423T223141
CREATED:20211230T013247Z
LAST-MODIFIED:20240705T180010Z
UID:5080-1643301000-1643304600@dimag.ibs.re.kr
SUMMARY:Bo Ning (宁博)\, Substructures and eigenvalues of graphs: Triangles and quadrilaterals
DESCRIPTION:Our talk will mainly focus on the relationship between substructures and eigenvalues of graphs. We will briefly survey recent developments on a conjecture of Bollobás and Nikiforov and a classical result of Nosal on triangles. In particular\, we shall present counting results for previous spectral theorems on triangles and quadrilaterals. If time allows\, we will give a sketch for the proof of one new counting result on triangles.
URL:https://dimag.ibs.re.kr/event/2022-01-27/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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