{"id":3843,"date":"2021-02-24T16:56:58","date_gmt":"2021-02-24T21:56:58","guid":{"rendered":"http:\/\/matroidunion.org\/?p=3843"},"modified":"2021-03-03T19:04:09","modified_gmt":"2021-03-04T00:04:09","slug":"online-talk-o-joung-kwon-at-5pm","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=3843","title":{"rendered":"Online talk: O-joung Kwon (at *5pm*)"},"content":{"rendered":"\n<p><strong>Monday, March 1,<\/strong> <strong>*****5pm ET<\/strong>***** (10pm GMT, 11am Tue NZDT)<br \/><a href=\"http:\/\/ojkwon.com\/\"><strong>O-joung Kwon<\/strong><\/a>, Incheon National University<br \/><strong>A unified half-integral Erd\u0151s-P\u00f3sa theorem for cycles in graphs labelled by multiple abelian groups<\/strong><\/p>\n<div>\n<div><b>YouTube: <\/b><a href=\"https:\/\/youtu.be\/lu4zG8MxgQ8\">https:\/\/youtu.be\/lu4zG8MxgQ8<\/a><\/div>\n<\/div>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<\/strong><\/h5>\n<p>Erd\u0151s and P\u00f3sa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles. However, in 1999, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a graph are labelled by finitely many abelian groups, then there is a duality between the maximum size of a half-integral packing of cycles whose values avoid a fixed finite set for each abelian group and the minimum size of a vertex set hitting all such cycles.<\/p>\n<p>A multitude of natural properties of cycles can be encoded in this setting, for example cycles of length at least $\\ell$, cycles of length $p$ modulo $q$, cycles intersecting a prescribed set of vertices at least $t$ times, and cycles contained in given $\\mathbb{Z}_2$-homology classes in a graph embedded on a fixed surface. Our main result allows us to prove a duality theorem for cycles satisfying a fixed set of finitely many such properties.<\/p>\n<p>This is joint work with J. Pascal Gollin, Kevin Hendrey, Ken-ichi Kawarabayashi, and Sang-il Oum.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Monday, March 1, *****5pm ET***** (10pm GMT, 11am Tue NZDT)O-joung Kwon, Incheon National UniversityA unified half-integral Erd\u0151s-P\u00f3sa theorem for cycles in graphs labelled by multiple abelian groups YouTube: https:\/\/youtu.be\/lu4zG8MxgQ8 \u00a0 Abstract: Erd\u0151s and P\u00f3sa proved in 1965 that there is &hellip; <a href=\"https:\/\/matroidunion.org\/?p=3843\">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-3843","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\/3843","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=3843"}],"version-history":[{"count":7,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3843\/revisions"}],"predecessor-version":[{"id":3868,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3843\/revisions\/3868"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3843"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3843"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}