# 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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Caccetta-Häggkvist conjecture is a longstanding open problem on degree conditions that force an oriented graph to contain a directed cycle of a bounded length. Motivated by this conjecture, Kelly,…

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