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DTSTART;TZID=Asia/Seoul:20210928T163000
DTEND;TZID=Asia/Seoul:20210928T173000
DTSTAMP:20260424T082005
CREATED:20210928T073000Z
LAST-MODIFIED:20240707T080955Z
UID:4452-1632846600-1632850200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, Extremal functions for sparse minors
DESCRIPTION:The extremal function $c(H)$ of a graph $H$ is the supremum of densities of graphs not containing $H$ as a minor\, where the density of a graph is the ratio of the number of edges to the number of vertices. Myers and Thomason (2005)\, Norin\, Reed\, Thomason and Wood (2020)\, and Thomason and Wales (2019) determined the asymptotic behaviour of $c(H)$ for all polynomially dense graphs $H$\, as well as almost all graphs of constant density. We explore the asymptotic behavior of the extremal function in the regime not covered by the above results\, where in addition to having constant density the graph $H$ is in a graph class admitting strongly sublinear separators. We establish asymptotically tight bounds in many cases. For example\, we prove that for every planar graph $H$\, \[c(H) = (1+o(1))\max (v(H)/2\, v(H)-\alpha(H))\,\] extending recent results of Haslegrave\, Kim and Liu (2020). Joint work with Sergey Norin and David R. Wood.
URL:https://dimag.ibs.re.kr/event/2021-09-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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