{"id":4602,"date":"2022-03-03T02:50:36","date_gmt":"2022-03-03T07:50:36","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4602"},"modified":"2022-03-13T18:53:34","modified_gmt":"2022-03-13T22:53:34","slug":"online-talk-sang-il-oum","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4602","title":{"rendered":"Online Talk: Sang-il Oum"},"content":{"rendered":"\n<p><strong>Tuesday, March 8, **4<\/strong><strong>pm ET**<\/strong> (9pm GMT, 10am Wed NZDT)<br \/><strong><a href=\"https:\/\/dimag.ibs.re.kr\/home\/sangil\/\">Sang-il Oum<\/a><\/strong>, Institute for Basic Science \/ KAIST<br \/><strong>Obstructions for matroids of path-width at most $k$ and graphs of linear rank-width at most $k$<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"https:\/\/youtu.be\/HOpekT8yCIo\">https:\/\/youtu.be\/HOpekT8yCIo<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><strong>Abstract:<\/strong><\/h5>\n<h5>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.<\/h5>\n<h5>\u00a0<\/h5>\n<h5>We 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.<\/h5>\n<h5>\u00a0<\/h5>\n<h5>This is joint work with Mamadou M. Kant\u00e9, Eun Jung Kim, and O-joung Kwon.<\/h5>\n","protected":false},"excerpt":{"rendered":"<p>Tuesday, March 8, **4pm ET** (9pm GMT, 10am Wed NZDT)Sang-il Oum, Institute for Basic Science \/ KAISTObstructions for matroids of path-width at most $k$ and graphs of linear rank-width at most $k$ YouTube: https:\/\/youtu.be\/HOpekT8yCIo \u00a0 Abstract: Every minor-closed class of &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4602\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":20,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-4602","post","type-post","status-publish","format-standard","hentry","category-matroids","tag-online-talks"],"_links":{"self":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4602","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4602"}],"version-history":[{"count":6,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4602\/revisions"}],"predecessor-version":[{"id":4621,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4602\/revisions\/4621"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4602"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}