List-coloring embedded graphs [chapter]

Zdeněk Dvořák, Ken-ichi Kawarabayashi
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
For any fixed surface Σ of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Σ is colorable from an assignment of lists of size three in time O(|V (G)|). Furthermore, we can allow a subgraph (of any size) with at most s components to be precolored, at the expense of increasing the time complexity of the algorithm to O |V (G)| K(g+s)+1 for some absolute constant K; in both cases, the multiplicative constant hidden in the O-notation depends on g and s.
more » ... is also enables us to find such a coloring when it exists. The idea of the algorithm can be applied to other similar problems, e.g., 5-list-coloring of graphs on surfaces. *
doi:10.1137/1.9781611973105.72 dblp:conf/soda/DvorakK13 fatcat:kc272dhajfajxh4ypvnauzd2ty