{"id":4071,"date":"2021-06-02T13:06:51","date_gmt":"2021-06-02T17:06:51","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4071"},"modified":"2021-06-07T22:35:01","modified_gmt":"2021-06-08T02:35:01","slug":"online-talk-abhinav-shantanam","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4071","title":{"rendered":"Online Talk: Abhinav Shantanam"},"content":{"rendered":"\n<p><strong>Monday, June 7,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 7am Tue NZST)<br \/><strong>Abhinav Shantanam<\/strong>, Simon Fraser University<br \/><strong>Pancyclicity in $4$-connected planar graphs<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"https:\/\/www.youtube.com\/watch?v=WtIIpPIIvwk\">https:\/\/www.youtube.com\/watch?v=WtIIpPIIvwk<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<br \/><\/strong>A graph on $n$ vertices is said to be pancyclic if, for each $k \\in \\{3,&#8230;,n\\}$, it contains\u00a0a cycle of length\u00a0$k$. Following Bondy&#8217;s meta-conjecture that almost any nontrivial condition on a graph which implies Hamiltonicity also implies pancyclicity, Malkevitch conjectured that a $4$-regular,\u00a0$4$-connected planar graph containing a $4$-cycle\u00a0is pancyclic. We show that, for any edge $e$ in a $4$-connected planar graph $G$, there exist\u00a0$\\lambda(n-2)$ cycles of pairwise distinct lengths containing $e$, where $5\/12 \\leq\u00a0\\lambda \\leq 2\/3$. Joint work with Bojan Mohar.<\/h5>\n","protected":false},"excerpt":{"rendered":"<p>Monday, June 7, 3pm ET (8pm BST, 7am Tue NZST)Abhinav Shantanam, Simon Fraser UniversityPancyclicity in $4$-connected planar graphs YouTube: https:\/\/www.youtube.com\/watch?v=WtIIpPIIvwk \u00a0 Abstract:A graph on $n$ vertices is said to be pancyclic if, for each $k \\in \\{3,&#8230;,n\\}$, it contains\u00a0a cycle &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4071\">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-4071","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\/4071","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=4071"}],"version-history":[{"count":2,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4071\/revisions"}],"predecessor-version":[{"id":4075,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4071\/revisions\/4075"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}