{"id":4279,"date":"2021-09-29T15:22:24","date_gmt":"2021-09-29T19:22:24","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4279"},"modified":"2021-10-06T23:41:05","modified_gmt":"2021-10-07T03:41:05","slug":"online-talk-jagdeep-singh","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4279","title":{"rendered":"Online Talk: Jagdeep Singh"},"content":{"rendered":"\n<p><strong>Tuesday, Oct 5,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 8am Wed NZST)<br \/><strong><a href=\"https:\/\/www.math.lsu.edu\/~jsing29\/\">Jagdeep Singh<\/a><\/strong>, Louisiana State University<br \/><b>$2$-Cographs and Binary Comatroids<\/b><\/p>\n<div><strong>YouTube:\u00a0<\/strong><a href=\"https:\/\/youtu.be\/EVzwtQ0cgOY\">https:\/\/youtu.be\/EVzwtQ0cgOY<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><strong>Abstract:<br \/><\/strong>The well-known class of cographs or complement-reducible graphs is the class of graphs that can be generated from $K_1$ using the operations of disjoint union and complementation. In this talk, we consider $2$-cographs, a natural generalization of cographs, and binary comatroids, a matroid analogue. We show that, as with cographs, both $2$-cographs and binary comatroids can be recursively defined. However, unlike cographs, $2$-cographs and binary comatroids are closed under induced minors. We consider the class of non-$2$-cographs for which every proper induced minor is a $2$-cograph and show that this class is infinite. Our main result for graphs finds the finitely many members of this class whose complements are also\u00a0 induced-minor-minimal non-$2$-cographs. In the matroid case, our main result identifies all binary non-comatroids for which every proper flat is a binary comatroid. This is joint work with James Oxley.<\/h5>\n<p>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tuesday, Oct 5, 3pm ET (8pm BST, 8am Wed NZST)Jagdeep Singh, Louisiana State University$2$-Cographs and Binary Comatroids YouTube:\u00a0https:\/\/youtu.be\/EVzwtQ0cgOY \u00a0 Abstract:The well-known class of cographs or complement-reducible graphs is the class of graphs that can be generated from $K_1$ using the &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4279\">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-4279","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\/4279","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=4279"}],"version-history":[{"count":2,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4279\/revisions"}],"predecessor-version":[{"id":4321,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4279\/revisions\/4321"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}