Acyclic Edge Colouring of Outerplanar Graphs

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) ≤ ∆(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(n log ∆) time algorithm. We also show that ∆ + 1 colours are sufficient for the class of fully subdevided graphs. Here, ∆ = ∆(G) denotes the maximum degree of the input graph.

• Type: Conference
• Year: 2007
• Where: AAIM
• Authors: Rahul Muthu, N. Narayanan, C. R. Subramanian
• Keywords: AAIM 2007, Acyclic Chromatic Index, Acyclic Edge Colouring, Algorithms, Proper Edge