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DTSTART:20240101T000000
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DTSTART;TZID=Asia/Seoul:20251028T163000
DTEND;TZID=Asia/Seoul:20251028T173000
DTSTAMP:20260416T111621
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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