# Linear-Time and Efficient Distributed Algorithms for List Coloring Graphs on Surfaces

@article{Postle2019LinearTimeAE, title={Linear-Time and Efficient Distributed Algorithms for List Coloring Graphs on Surfaces}, author={Luke Postle}, journal={2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)}, year={2019}, pages={929-941} }

In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs naturally lead to quadratic-time algorithms to find such colorings. Here, we provide the first linear-time algorithms to find such colorings. For a fixed surface S, Thomassen showed in 1997 that there exists a linear-time algorithm to decide if a graph embedded in S is 5-colorable and similarly in 2003 if a graph of girth… Expand

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