List Conflict-free Coloring
<|reference_start|>List Conflict-free Coloring: Motivated by its application in the frequency assignment problem for cellular networks, conflict-free coloring was first studied by Even et al. in [Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks, SIAM Journal on Computing, 2004]. A \emph{conflict-free coloring} of a hypergraph $\mathcal{H}$ is an assignment of colors to the vertex set of $\mathcal{H}$ such that every hyperedge in $\mathcal{H}$ has a vertex whose color is distinct from every other vertex in that hyperedge. The minimum number of colors required for such a coloring is known as the \emph{conflict-free chromatic number} of $\mathcal{H}$. Conflict-free coloring has also been studied on open/closed neighborhood hypergraphs of a given graph.   In this paper, we study the list variant of conflict-free coloring where, for every vertex $v$, we are given a list of admissible colors $L_v$ such that $v$ is allowed to be colored only from $L_v$. We prove upper bounds for the list conflict-free chromatic number of general hypergraphs and graphs.<|reference_end|>
@article{gupta2024list,
    title={List Conflict-free Coloring},
    author={Shiwali Gupta and Rogers Mathew},
    journal={arXiv preprint arXiv:2409.12672},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12672},
    primaryClass={math.CO cs.DM}
}