{"id":3202,"date":"2020-09-23T11:05:06","date_gmt":"2020-09-23T15:05:06","guid":{"rendered":"http:\/\/matroidunion.org\/?p=3202"},"modified":"2020-10-16T11:50:13","modified_gmt":"2020-10-16T15:50:13","slug":"online-talk-dan-cranston","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=3202","title":{"rendered":"Online talk: Dan Cranston"},"content":{"rendered":"\n<h5><strong>Monday, September 28,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 7am Tue NZST)<br \/><strong><a href=\"https:\/\/www.people.vcu.edu\/~dcranston\/\">Dan Cranston<\/a><\/strong>, Virginia Commonwealth U<br \/><strong>Vertex Partitions into an Independent Set and a Forest with Each Component Small<br \/><a href=\"https:\/\/www.youtube.com\/watch?v=w5oja61pDpA&amp;list=PL_x-9BL_zf4E6rsM9-9Gk6ft8H3t-ylCr&amp;index=21\">Youtube<\/a><\/strong><b><\/b><\/h5>\n<p>\u00a0<\/p>\n<p><strong>Abstract:<br \/><\/strong>For each integer $k \\ge 2$, we determine a sharp bound on $\\text{mad}(G)$ such that $V(G)$ can be partitioned into sets $I$ and $F_k$, where $I$ is an independent set and $G[F_k]$ is a forest in which each component has at most $k$ vertices. For each $k$ we construct an infinite family of examples showing our result is best possible. Hendrey, Norin, and Wood asked for the largest function $g(a,b)$ such that if $\\text{mad}(G)&lt;g(a,b)$ then $V(G)$ has a partition into sets $A$ and $B$ such that $\\text{mad}(G[A])&lt;a$ and $\\text{mad}(G[B])&lt;b$. They specifically asked for the value of $g(1,b)$, which corresponds to the case that $A$ is an independent set. Previously, the only values known were $g(1,4\/3)$ and $g(1,2)$. We find the value of $g(1,b)$ whenever $4\/3&lt;b&lt;2$. This is joint work with Matthew Yancey.<br \/><br \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Monday, September 28, 3pm ET (8pm BST, 7am Tue NZST)Dan Cranston, Virginia Commonwealth UVertex Partitions into an Independent Set and a Forest with Each Component SmallYoutube \u00a0 Abstract:For each integer $k \\ge 2$, we determine a sharp bound on $\\text{mad}(G)$ &hellip; <a href=\"https:\/\/matroidunion.org\/?p=3202\">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-3202","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\/3202","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=3202"}],"version-history":[{"count":5,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3202\/revisions"}],"predecessor-version":[{"id":3240,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/3202\/revisions\/3240"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3202"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3202"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}