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AAIM
2007
Springer

Acyclic Edge Colouring of Outerplanar Graphs

10 years 4 months ago
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.
Rahul Muthu, N. Narayanan, C. R. Subramanian
Added 06 Jun 2010
Updated 06 Jun 2010
Type Conference
Year 2007
Where AAIM
Authors Rahul Muthu, N. Narayanan, C. R. Subramanian
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