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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Muthu, R., Narayanan, N., Subramanian, C.R. (2007). Acyclic Edge Colouring of Outerplanar Graphs. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_14
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DOI: https://doi.org/10.1007/978-3-540-72870-2_14
Publisher Name: Springer, Berlin, Heidelberg
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