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Acyclic Edge Colouring of Outerplanar Graphs

  • Rahul Muthu
  • N. Narayanan
  • C. R. Subramanian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4508)

Abstract

An acyclic edge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge colouring using k colours and is usually denoted by a′(G). Determining a′(G) exactly is a very hard problem (both theoretically and algorithmically) and is not determined even for complete graphs. We show that a′(G) ≤ Δ(G) + 1, if G is an outerplanar graph. This bound is tight within an additive factor of 1 from optimality. Our proof is constructive leading to an \(O\!\left({n \log \Delta}\right)\) time algorithm. Here, Δ = Δ(G) denotes the maximum degree of the input graph.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Rahul Muthu
    • 1
  • N. Narayanan
    • 1
  • C. R. Subramanian
    • 1
  1. 1.The Institute of Mathematical Sciences, ChennaiIndia

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