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:20210101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220228T163000
DTEND;TZID=Asia/Seoul:20220228T173000
DTSTAMP:20260423T172214
CREATED:20220228T073000Z
LAST-MODIFIED:20240707T080351Z
UID:5298-1646065800-1646069400@dimag.ibs.re.kr
SUMMARY:Sang-il Oum (엄상일)\, Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k
DESCRIPTION:Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors\, but unlike graphs\, this list could be infinite in general. However\, for each fixed finite field $\mathbb F$\, the list contains only finitely many $\mathbb F$-representable matroids\, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen\, A. M. H. Gerards\, and G. Whittle (2002)]. But this proof is non-constructive and does not provide any algorithm for computing these $\mathbb F$-representable excluded minors in general. \nWe consider the class of matroids of path-width at most $k$ for fixed $k$. We prove that for a finite field $\mathbb F$\, every $\mathbb F$-representable excluded minor for the class of matroids of path-width at most~$k$ has at most $2^{|\mathbb{F}|^{O(k^2)}}$ elements. We can therefore compute\, for any integer $k$ and a fixed finite field $\mathbb F$\, the set of $\mathbb F$-representable excluded minors for the class of matroids of path-width $k$\, and this gives as a corollary a polynomial-time algorithm for checking whether the path-width of an $\mathbb F$-represented matroid is at most $k$. We also prove that every excluded pivot-minor for the class of graphs having linear rank-width at most $k$ has at most $2^{2^{O(k^2)}}$ vertices\, which also results in a similar algorithmic consequence for linear rank-width of graphs. \nThis is joint work with Mamadou M. Kanté\, Eun Jung Kim\, and O-joung Kwon.
URL:https://dimag.ibs.re.kr/event/2022-02-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR