Conflict-free chromatic index of trees
<|reference_start|>Conflict-free chromatic index of trees: A graph $G$ is conflict-free $k$-edge-colorable if there exists an assignment of $k$ colors to $E(G)$ such that for every edge $e\in E(G)$, there is a color that is assigned to exactly one edge among the closed neighborhood of $e$. The smallest $k$ such that $G$ is conflict-free $k$-edge-colorable is called the conflict-free chromatic index of $G$, denoted $\chi'_{CF}(G)$. D\c{e}bski and Przyby\a{l}o showed that $2\le\chi'_{CF}(T)\le 3$ for every tree $T$ of size at least two. In this paper, we present an algorithm to determine the conflict-free chromatic index of a tree without 2-degree vertices, in time $O(|V(T)|)$. This partially answer a question raised by Kamyczura, Meszka and Przyby\a{l}o.<|reference_end|>
@article{guo2024conflict-free,
    title={Conflict-free chromatic index of trees},
    author={Shanshan Guo, Ethan Y.H. Li, Luyi Li, Ping Li},
    journal={arXiv preprint arXiv:2409.10899},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.10899},
    primaryClass={cs.DM math.CO}
}