Local Conflict Coloring Revisited: Linial for Lists

@inproceedings{Maus2020LocalCC,
  title={Local Conflict Coloring Revisited: Linial for Lists},
  author={Yannic Maus and Tigran Tonoyan},
  booktitle={DISC},
  year={2020}
}
Linial's famous color reduction algorithm reduces a given $m$-coloring of a graph with maximum degree $\Delta$ to a $O(\Delta^2\log m)$-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to choose their color from a list of allowed colors: given an $m$-coloring in a directed graph of maximum outdegree $\beta$, if every node has a list of size $\Omega(\beta^2 (\log \beta+\log\log m + \log \log |\mathcal{C}|))$ from a color space $\mathcal{C}$ then… 
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