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- W2063861912 abstract "An acyclic coloring of a graph G is a coloring of the vertices of G, where no two adjacent vertices of G receive the same color and no cycle of G is bichromatic. An acyclic k-coloring of G is an acyclic coloring of G using at most k colors. In this paper we prove that any triangulated plane graph G with n vertices has a subdivision that is acyclically 3-colorable, where the number of division vertices is at most 2.75n−6. This upper bound on the number of division vertices reduces to 2n−6 in the case of acyclic 4-coloring. We show that it is NP-complete to decide whether a graph with degree at most 6 is acyclically 4-colorable or not. Furthermore, we give some upper bounds on the number of division vertices for acyclic 3-coloring of subdivisions of k-trees and cubic graphs." @default.
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- W2063861912 date "2012-10-01" @default.
- W2063861912 modified "2023-09-30" @default.
- W2063861912 title "Acyclic colorings of graph subdivisions revisited" @default.
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- W2063861912 doi "https://doi.org/10.1016/j.jda.2012.06.001" @default.
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