2026.02.03, Xiaofan Yuan, Rainbow structures in edge colored graphs скачать в хорошем качестве

2026.02.03, Xiaofan Yuan, Rainbow structures in edge colored graphs

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.