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 4-colorable, where the number of division vertices is at most 2n − 6. We show that it is NP-complete to decide whether a graph with degree at most 7 is acyclically 4-colorable or not. Furthermore, we give some sufficient conditions on the number of division vertices for acyclic 3-coloring of subdivisions of partial k-trees and cubic graphs.
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Mondal, D., Nishat, R.I., Whitesides, S., Rahman, M.S. (2011). Acyclic Colorings of Graph Subdivisions. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_20
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DOI: https://doi.org/10.1007/978-3-642-25011-8_20
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