2026.02.03, Xiaofan Yuan, Rainbow structures in edge colored graphs
Автор: IBS Discrete Mathematics Group
Загружено: 2026-02-02
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Xiaofan Yuan, Rainbow structures in edge colored graphs
February 3 Tuesday @ 4:30 PM - 5:30 PM KST
Room B332, IBS (기초과학연구원)
Xiaofan Yuan
IBS Extremal Combinatorics and Probability Group
https://math.la.asu.edu/~xyuan/
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.
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