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)


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.


Acyclic coloring Subdivision Triangulated plane graph 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

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

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