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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260203T163000
DTEND;TZID=Asia/Seoul:20260203T173000
DTSTAMP:20260415T152551
CREATED:20260105T005335Z
LAST-MODIFIED:20260105T054623Z
UID:12035-1770136200-1770139800@dimag.ibs.re.kr
SUMMARY:Xiaofan Yuan (袁晓璠)\, Rainbow structures in edge colored graphs
DESCRIPTION:Let $G = (V\, E)$ be a graph on $n$ vertices\, and let $c : E \to P$\, where $P$ is a set of colors. Let $\delta^c(G) = \min_{v \in V} \{ d^{c}(v) \}$ where $d^c(v)$ is the number of colors on edges incident to a vertex $v$ of $G$. In 2011\, Fujita and Magnant showed that if $G$ is a graph on $n$ vertices that satisfies $\delta^c(G)\geq n/2$\, then for every two vertices $u\, v$ there is a properly-colored $u\,v$-path in $G$. We show that for sufficiently large graphs $G$\, the same bound for $\delta^c(G)$ implies that any two vertices are connected by a rainbow path. We also show sufficient conditions on $\delta^c(G)$ for the existence of a rainbow cycle of length $2k$ in sufficiently large bipartite graphs $G$\, which are tight in many cases. This is joint work with Andrzej Czygrinow.
URL:https://dimag.ibs.re.kr/event/2026-02-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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