About acyclic edge colourings of planar graphs

  • Authors:

  • Anna Fiedorowicz;Mariusz Hałuszczak;Narayanan Narayanan

  • Affiliations:

  • Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Z. Szafrana 4a, Zielona Góra, Poland;Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Z. Szafrana 4a, Zielona Góra, Poland;The Institute of Mathematical Sciences, Chennai, India

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

Quantified Score

Hi-index 0.89

Visualization

Abstract

Let G=(V,E) be any finite simple graph. A mapping C:E-[k] is called an acyclic edge k-colouring of G, if any two adjacent edges have different colours and there are no bichromatic cycles in G. In other words, for every pair of distinct colours i and j, the subgraph induced by all the edges which have either colour i or j is acyclic. The smallest number k of colours, such that G has an acyclic edge k-colouring is called the acyclic chromatic index of G and is denoted by @g"a^'(G). In 1991, Alon et al. [N. Alon, C.J.H. McDiarmid, B.A. Reed, Acyclic coloring of graphs, Random Structures and Algorithms 2 (1991) 277-288] proved that @g"a^'(G)=