IWOCA 2011: Combinatorial Algorithms pp 247-260

# Acyclic Colorings of Graph Subdivisions

• Debajyoti Mondal
• Rahnuma Islam Nishat
• Sue Whitesides
• Md. Saidur Rahman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)

## 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.

## Keywords

Acyclic coloring Subdivision Triangulated plane graph

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## Authors and Affiliations

• Debajyoti Mondal
• 1
• Rahnuma Islam Nishat
• 2
• Sue Whitesides
• 2
• Md. Saidur Rahman
• 3
1. 1.Department of Computer ScienceUniversity of ManitobaCanada
2. 2.Department of Computer ScienceUniversity of VictoriaCanada
3. 3.Department of Computer Science and EngineeringBangladesh University of Engineering and Technology (BUET)Bangladesh