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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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DTSTART:20240101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20251014T163000
DTEND;TZID=Asia/Seoul:20251014T173000
DTSTAMP:20260416T124010
CREATED:20250918T011807Z
LAST-MODIFIED:20250918T014049Z
UID:11604-1760459400-1760463000@dimag.ibs.re.kr
SUMMARY:Ilkyoo Choi (최일규)\, An improved lower bound on the number of edges in list critical graphs via DP coloring
DESCRIPTION:A graph $G$ is (list\, DP) $k$-critical if the (list\, DP) chromatic number is $k$ but for every proper subgraph $G’$ of $G$\, the (list\, DP) chromatic number of $G’$ is less than $k$. For $k\geq 4$\, we show a bound on the minimum number of edges in a DP $k$-critical graph\, and our bound is the first bound that is asymptotically better than the corresponding bound for proper $k$-critical graphs by Gallai from 1963. Our result also improves the best bound on the list chromatic number. This is joint work with Bradshaw\, Kostochka\, and Xu.
URL:https://dimag.ibs.re.kr/event/2025-10-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20251021T163000
DTEND;TZID=Asia/Seoul:20251021T173000
DTSTAMP:20260416T124010
CREATED:20250622T150459Z
LAST-MODIFIED:20250918T235327Z
UID:11035-1761064200-1761067800@dimag.ibs.re.kr
SUMMARY:William Cook\, Optimization via Branch Decomposition
DESCRIPTION:Robertson and Seymour introduced branch-width as a connectivity invariant of graphs in their proof of the Wagner conjecture. Decompositions based on this invariant provide a natural framework for implementing dynamic-programming algorithms to solve graph optimization problems. We will discuss the computational issues involved in using branch-width as as a general tool in discrete optimization.
URL:https://dimag.ibs.re.kr/event/2025-10-21/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20251028T163000
DTEND;TZID=Asia/Seoul:20251028T173000
DTSTAMP:20260416T124010
CREATED:20250930T125827Z
LAST-MODIFIED:20251028T061518Z
UID:11672-1761669000-1761672600@dimag.ibs.re.kr
SUMMARY:Jakob Greilhuber\, A Dividing Line for Structural Kernelization of Component Order Connectivity via Distance to Bounded Pathwidth
DESCRIPTION:Vertex Cover is perhaps the most-studied problem in parameterized complexity that frequently serves as a testing ground for new concepts and techniques. In this talk\, I will focus on a generalization of Vertex Cover called Component Order Connectivity (COC). Given a graph G\, an integer k and a positive integer d\, the task is to decide whether there is a vertex set S of size at most k such that each connected component of G – S has size at most d. If d = 1\, then COC is the same as Vertex Cover. \nWhile almost all techniques to obtain polynomial kernels for Vertex Cover extend well to COC parameterized by k + d\, the same cannot be said for structural parameters. Vertex Cover admits a polynomial kernel parameterized by the vertex deletion distance to treewidth 1 graphs\, but not when parameterized by the deletion distance to treewidth 2 graphs. The picture changes when considering COC: It was recently shown that COC does not admit a polynomial kernel parameterized by the vertex deletion distance to treewidth 1 graphs with pathwidth 2\, even if d ≥ 2 is a fixed constant. \nComplementing this\, we show that COC does admit a polynomial kernel parameterized by the distance to graphs with pathwidth at most 1 (plus d). Hence\, the deletion distance to pathwidth 1 vs. pathwidth 2 forms a similar line of tractability for COC as the distance to treewidth 1 vs. treewidth 2 does for Vertex Cover. In this talk\, I will highlight the ideas and techniques that make this kernelization result possible.
URL:https://dimag.ibs.re.kr/event/2025-10-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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