{"id":2791,"date":"2020-08-25T09:48:36","date_gmt":"2020-08-25T13:48:36","guid":{"rendered":"http:\/\/matroidunion.org\/?p=2791"},"modified":"2020-09-03T12:10:01","modified_gmt":"2020-09-03T16:10:01","slug":"online-talk-tony-huynh","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=2791","title":{"rendered":"Online talk: Tony Huynh"},"content":{"rendered":"\n<p><strong>Mon, August 31,<\/strong> 3pm ET (8pm BST, 7am Tue NZST)<br \/><a href=\"https:\/\/sites.google.com\/site\/matroidintersection\/\"><strong>Tony Huynh<\/strong><\/a>, Monash University<br \/><strong>Subgraph densities in a surface<br \/><\/strong><a href=\"https:\/\/youtu.be\/385YEj1t_Lg\"><strong>Youtube<\/strong><\/a><b><\/b><\/p>\n<p><strong>Abstract:<br \/><\/strong>We consider the following problem at the intersection of extremal and structural graph theory. Given a fixed graph $H$ and surface $\\Sigma$, what is the maximum number of copies of $H$ in an $n$-vertex graph that embeds in $\\Sigma$? Here a <em>copy<\/em> means a subgraph isomorphic to $H$. Exact answers are known for some $H$ when $\\Sigma$ is the sphere. Our main result answers the question for all $H$ and $\\Sigma$ (up to a constant factor). We show that the answer is $\\Theta(n^{f(H)})$ where $f(H)$ is a graph invariant called the <em>flap number<\/em> of $H$, which is independent of the surface $\\Sigma$.<\/p>\n<p>This is joint work with Gwena\u00ebl Joret and David Wood.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mon, August 31, 3pm ET (8pm BST, 7am Tue NZST)Tony Huynh, Monash UniversitySubgraph densities in a surfaceYoutube Abstract:We consider the following problem at the intersection of extremal and structural graph theory. Given a fixed graph $H$ and surface $\\Sigma$, what &hellip; <a href=\"https:\/\/matroidunion.org\/?p=2791\">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-2791","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\/2791","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=2791"}],"version-history":[{"count":4,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2791\/revisions"}],"predecessor-version":[{"id":2882,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/2791\/revisions\/2882"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}