2012/10/29 by Zdenek Dvorak, Ken-ichi Kawarabayashi, Dvorak, Zdenek +1
Computer Science · Mathematics · #05C15 (Primary) 05C85 (Secondary) #Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #FOS: Mathematics #G.2.2 #acm:05C15 #acm:05C85 #cs.DS #math.CO #msc:05C15 #msc:05C85
paper · pdf · doi:10.48550/arxiv.1210.7605
14 pages, 0 figures, accepted to SODA'13
arxiv created 2012/10/29 · arxiv updated 2012/10/30
For any fixed surface Sigma of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Sigma 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. This 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.