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TZOFFSETFROM:+0900
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DTSTART:20190101T000000
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DTSTART;TZID=Asia/Seoul:20200414T163000
DTEND;TZID=Asia/Seoul:20200414T173000
DTSTAMP:20260420T082315
CREATED:20200409T030201Z
LAST-MODIFIED:20240705T201139Z
UID:2322-1586881800-1586885400@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, Saturation problems in the Ramsey theory of graphs\, posets and point sets
DESCRIPTION:In 1964\, Erdős\, Hajnal and Moon introduced a saturation version of Turán’s classical theorem in extremal graph theory. In particular\, they determined the minimum number of edges in a $K_r$-free\, $n$-vertex graph with the property that the addition of any further edge yields a copy of $K_r$. We consider analogues of this problem in other settings. We prove a saturation version of the Erdős-Szekeres theorem about monotone subsequences and saturation versions of some Ramsey-type theorems on graphs and Dilworth-type theorems on posets. \nWe also consider semisaturation problems\, wherein we allow the family to have the forbidden configuration\, but insist that any addition to the family yields a new copy of the forbidden configuration. In this setting\, we prove a semisaturation version of the Erdős-Szekeres theorem on convex $k$-gons\, as well as multiple semisaturation theorems for sequences and posets. \nThis project was joint work with Gábor Damásdi\, Balázs Keszegh\, David Malec\, Zhiyu Wang and Oscar Zamora.
URL:https://dimag.ibs.re.kr/event/2020-04-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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