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Acyclic coloring with few division vertices
2013
Journal of Discrete Algorithms
An acyclic k-coloring of a graph G is a mapping φ from the set of vertices of G to a set of k distinct colors such that no two adjacent vertices receive the same color and φ does not contain any bichromatic cycle. In this paper we prove that every triangulated plane graph with n vertices has a 1-subdivision that is acyclically 3-colorable (respectively, 4-colorable), where the number of division vertices is at most 2n − 5 (respectively, 1.5n − 3.5). Our results imply O(n log 16 n) and O(n log
doi:10.1016/j.jda.2013.08.002
fatcat:t465grxbofhl7hcik22p7kefry