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Acyclic Coloring with Few Division Vertices

  • Debajyoti Mondal
  • Rahnuma Islam Nishat
  • Md. Saidur Rahman
  • Sue Whitesides
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

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 (respectively, 0.3n) lower bound on the number of division vertices for acyclic 3-colorings (respectively, 4-colorings) of triangulated planar graphs. Furthermore, we establish the NP-completeness of deciding acyclic 4-colorability for graphs with the maximum degree 5 and for planar graphs with the maximum degree 7.

Keywords

Planar Graph Maximum Degree Outer Face Outer Vertex Bipartite Planar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Debajyoti Mondal
    • 1
  • Rahnuma Islam Nishat
    • 2
  • Md. Saidur Rahman
    • 3
  • Sue Whitesides
    • 2
  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada
  2. 2.Department of Computer ScienceUniversity of VictoriaVictoriaCanada
  3. 3.Department of Computer Science and EngineeringBangladesh University of Engineering and TechnologyDhakaBangladesh

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