{"id":4957,"date":"2023-06-16T10:41:39","date_gmt":"2023-06-16T14:41:39","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4957"},"modified":"2023-06-22T19:59:11","modified_gmt":"2023-06-22T23:59:11","slug":"online-talk-tung-nguyen","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4957","title":{"rendered":"Online Talk: Tung Nguyen"},"content":{"rendered":"\n<p><strong>YouTube recording:\u00a0<\/strong><a href=\"https:\/\/www.youtube.com\/watch?v=9nzX08hoQEw\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=9nzX08hoQEw<\/a><\/p>\n<p><strong>Time: <\/strong>Thursday, June 22, 3pm ET<br \/><strong>Zoom: <\/strong><a href=\"https:\/\/gatech.zoom.us\/j\/8802082683\" target=\"_blank\" rel=\"noopener\">https:\/\/gatech.zoom.us\/j\/8802082683<\/a><\/p>\n<p><strong>Speaker: <\/strong><a href=\"https:\/\/web.math.princeton.edu\/~tunghn\/\" target=\"_blank\" rel=\"noopener\">Tung Nguyen<\/a>, Princeton University<br \/><strong>Title: <\/strong>More graphs with the Erd\u0151s\u2013Hajnal property<br \/><br \/><strong>Abstract: <\/strong>Erd\u0151s and Hajnal conjectured that for every graph $H$, there exists $c&gt;0$ such that every $n$-vertex graph with no induced copy of $H$ contains a clique or stable set of size at least $n^c$. Alon, Pach, and Solymosi reduced this conjecture to the case when $H$ is prime, or equivalently when $H$ is not a blow-up of smaller graphs. Until now, it was not known for any prime $H$ on at least six vertices. This talk describes a construction of infinitely many prime graphs $H$ each satisfying the Erd\u0151s\u2013Hajnal conjecture. The proof method actually gives the stronger result that every such $H$ is viral, which will be explained in the talk. Joint work with Alex Scott and Paul Seymour.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YouTube recording:\u00a0https:\/\/www.youtube.com\/watch?v=9nzX08hoQEw Time: Thursday, June 22, 3pm ETZoom: https:\/\/gatech.zoom.us\/j\/8802082683 Speaker: Tung Nguyen, Princeton UniversityTitle: More graphs with the Erd\u0151s\u2013Hajnal property Abstract: Erd\u0151s and Hajnal conjectured that for every graph $H$, there exists $c&gt;0$ such that every $n$-vertex graph with no &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4957\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":21,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-4957","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\/4957","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\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4957"}],"version-history":[{"count":5,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4957\/revisions"}],"predecessor-version":[{"id":4968,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4957\/revisions\/4968"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}