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Acyclic Coloring with Few Division Vertices
[chapter]
2012
Lecture Notes in Computer Science
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). On the other hand, we prove an 1.28n
doi:10.1007/978-3-642-35926-2_11
fatcat:b6kdafg26zajzexo3qr45ms5ge