{"id":3922,"date":"2021-04-08T10:53:47","date_gmt":"2021-04-08T14:53:47","guid":{"rendered":"http:\/\/matroidunion.org\/?p=3922"},"modified":"2021-04-15T11:12:27","modified_gmt":"2021-04-15T15:12:27","slug":"online-talk-daryl-funk","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=3922","title":{"rendered":"Online talk: Daryl Funk"},"content":{"rendered":"\n<p><strong>Monday, April 12,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 7am Tue NZST)<br \/><a href=\"https:\/\/sites.google.com\/site\/darylfunk\/\"><strong>Daryl Funk<\/strong><\/a>, Douglas College<br \/><strong>The class of bicircular matroids has only a finite number of excluded minors<\/strong><\/p>\n<div><strong>YouTube:<\/strong><a href=\"https:\/\/youtu.be\/FRUjGKw8OCw\"> https:\/\/youtu.be\/FRUjGKw8OCw<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<\/strong><\/h5>\n<p>We show that the class of bicircular matroids has only a finite number of excluded minors. Key tools used in our proof include representations of matroids by biased graphs and the recently introduced class of quasi-graphic matroids. We show that if $N$ is an excluded minor of rank at least eight, then $N$ is quasi-graphic. Several small excluded minors are quasi-graphic. Using biased-graphic representations, we find that $N$ already contains one of these. We also provide an upper bound, in terms of rank, on the number of elements in an excluded minor, so the result follows.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Monday, April 12, 3pm ET (8pm BST, 7am Tue NZST)Daryl Funk, Douglas CollegeThe class of bicircular matroids has only a finite number of excluded minors YouTube: https:\/\/youtu.be\/FRUjGKw8OCw \u00a0 Abstract: We show that the class of bicircular matroids has only a &hellip; <a href=\"https:\/\/matroidunion.org\/?p=3922\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-3922","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\/3922","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3922"}],"version-history":[{"count":5,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3922\/revisions"}],"predecessor-version":[{"id":3935,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3922\/revisions\/3935"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}