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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201201T163000
DTEND;TZID=Asia/Seoul:20201201T173000
DTSTAMP:20260419T171021
CREATED:20201115T235924Z
LAST-MODIFIED:20240705T193016Z
UID:3273-1606840200-1606843800@dimag.ibs.re.kr
SUMMARY:Debsoumya Chakraborti\, Rainbow matchings in edge-colored simple graphs
DESCRIPTION:There has been much research on finding a large rainbow matching in a properly edge-colored graph\, where a proper edge coloring is a coloring of the edge set such that no same-colored edges are incident. Barát\, Gyárfás\, and Sárközy conjectured that in every proper edge coloring of a multigraph (with parallel edges allowed\, but not loops) with $2q$ colors where each color appears at least $q$ times\, there is always a rainbow matching of size $q$. We prove that $2q + o(q)$ colors are enough if the graph is simple\, confirming the conjecture asymptotically for simple graphs. We also make progress in the lower bound on the required number of colors for simple graphs\, which disproves a conjecture of Aharoni and Berger. We use a randomized algorithm to obtain a large rainbow matching\, and the analysis of the algorithm is based on differential equations method. We will also briefly comment on the limitations of using our probabilistic approach for the problem. This talk will be based on a joint work with Po-Shen Loh.
URL:https://dimag.ibs.re.kr/event/2020-12-01/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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