{"id":4077,"date":"2021-06-09T12:57:33","date_gmt":"2021-06-09T16:57:33","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4077"},"modified":"2021-06-14T17:36:01","modified_gmt":"2021-06-14T21:36:01","slug":"online-talk-youngho-yoo","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4077","title":{"rendered":"Online Talk: Youngho Yoo"},"content":{"rendered":"\n<p><strong>Monday, June 14,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 7am Tue NZST)<br \/><a href=\"https:\/\/people.math.gatech.edu\/~yyoo41\/\"><b>Youngho Yoo<\/b><\/a>, Georgia Tech<br \/><strong>Packing A-paths of length 0 modulo a prime<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"_wp_link_placeholder\" data-wplink-edit=\"true\">https:\/\/www.youtube.com\/watch?v=6zC2oAIllLE<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<\/strong><\/h5>\n<h5>An $A$-path is a nontrivial path with its endpoints in a vertex set $A$ that is internally disjoint from $A$. In 1961, Gallai showed that $A$-paths satisfy an approximate packing-covering duality,\u00a0also known as the\u00a0Erd\u0151s-P\u00f3sa property. There are many generalizations and variants of this result. In this talk, we show that the\u00a0Erd\u0151s-P\u00f3sa\u00a0property holds for $A$-paths of length 0 mod $p$ for every prime $p$, answering a question of Bruhn and Ulmer. The proof uses structure theorems for undirected group-labelled graphs. We also give a characterization of abelian groups $\\Gamma$ and elements $\\ell \\in \\Gamma$ for which the\u00a0Erd\u0151s-P\u00f3sa\u00a0property holds for\u00a0$A$-paths of weight $\\ell$ in undirected $\\Gamma$-labelled graphs. Joint work with Robin Thomas.<\/h5>\n","protected":false},"excerpt":{"rendered":"<p>Monday, June 14, 3pm ET (8pm BST, 7am Tue NZST)Youngho Yoo, Georgia TechPacking A-paths of length 0 modulo a prime YouTube: https:\/\/www.youtube.com\/watch?v=6zC2oAIllLE \u00a0 Abstract: An $A$-path is a nontrivial path with its endpoints in a vertex set $A$ that is &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4077\">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-4077","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\/4077","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=4077"}],"version-history":[{"count":3,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4077\/revisions"}],"predecessor-version":[{"id":4083,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4077\/revisions\/4083"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4077"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4077"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4077"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}