On even rainbow or nontriangular directed cycles

@article{Czygrinow2021OnER,
  title={On even rainbow or nontriangular directed cycles},
  author={Andrzej Czygrinow and Theodore Molla and Brendan Nagle and Roy Oursler},
  journal={Journal of Combinatorics},
  year={2021}
}
Let $G = (V, E)$ be an $n$-vertex edge-colored graph. In 2013, H. Li proved that if every vertex $v \in V$ is incident to at least $(n+1)/2$ distinctly colored edges, then $G$ admits a rainbow triangle. We establish a corresponding result for fixed even rainbow $\ell$-cycles $C_{\ell}$: if every vertex $v \in V$ is incident to at least $(n+5)/3$ distinctly colored edges, where $n \geq n_0(\ell)$ is sufficiently large, then $G$ admits an even rainbow $\ell$-cycle $C_{\ell}$. This result is best… 

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