{"id":4537,"date":"2022-01-05T15:29:26","date_gmt":"2022-01-05T20:29:26","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4537"},"modified":"2022-01-13T01:09:56","modified_gmt":"2022-01-13T06:09:56","slug":"online-talk-amena-assem","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4537","title":{"rendered":"Online Talk: Amena Assem"},"content":{"rendered":"\n<p><strong>Tuesday, Jan 11,<\/strong> <strong>3pm ET<\/strong> (8pm GMT, 9am Wed NZDT)<br \/><strong><a href=\"https:\/\/www.amenaassem.com\/\">Amena Assem<\/a><\/strong>, University of Waterloo<br \/><strong>Edge-Disjoint Linkage in Infinite Graphs<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"https:\/\/youtu.be\/gTzJWlxOguA\">https:\/\/youtu.be\/gTzJWlxOguA<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><strong>Abstract:<\/strong><\/h5>\n<h5>In 1980 Thomassen conjectured that, for odd $k$, an edge-connectivity of $k$ is enough for a graph to be weakly $k$-linked, meaning any $k$ pairs of terminals can be linked by $k$ edge-disjoint paths. The best known result to date for finite graphs is from 1991, by Andreas Huck, and assumes an edge-connectivity of $k+1$ for odd $k$. In 2016, Ok, Richter, and Thomassen proved that, for odd $k$, an edge-connectivity of $k+2$ implies weak $k$-linkage for $1$-ended locally finite graphs. An important auxiliary graph in edge-connectivity proofs is the lifting graph. <br \/>In this talk I will show how to reduce the connectivity condition in the result of Ok, Richter, and Thomassen to $k+1$, and then how to generalize to arbitrary infinite graphs, not necessarily locally finite, and possibly with uncountably many ends. I will also prove an extension of a result of Ok, Richter, and Thomassen about characterizing lifting graphs, and show that if the $k$-lifting graph of $G$ at $s$, $L(G,s,k)$, has a connected complement, then the graph $G$ has either a cycle-like or path-like structure around $s$ with $(k-1)\/2$ edges between any two consecutive blobs. Finally, will show how this structure might be used to prove that the conjecture for finite graphs implies the conjecture for infinite graphs.<\/h5>\n<p>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tuesday, Jan 11, 3pm ET (8pm GMT, 9am Wed NZDT)Amena Assem, University of WaterlooEdge-Disjoint Linkage in Infinite Graphs YouTube: https:\/\/youtu.be\/gTzJWlxOguA \u00a0 Abstract: In 1980 Thomassen conjectured that, for odd $k$, an edge-connectivity of $k$ is enough for a graph to &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4537\">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-4537","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\/4537","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=4537"}],"version-history":[{"count":4,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4537\/revisions"}],"predecessor-version":[{"id":4547,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4537\/revisions\/4547"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}