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- W2000814123 abstract "Let G be any finite graph. A mapping c:E(G)->{1,...,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 in G by all the edges that have 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 @ga^'(G). Determining the acyclic chromatic index of a graph is a hard problem, both from theoretical and algorithmical point of view. In 1991, Alon et al. proved that @ga^'(G)=<[email protected](G) for any graph G of maximum degree @D(G). This bound was later improved to [email protected](G) by Molloy and Reed. In general, the problem of computing the acyclic chromatic index of a graph is NP-complete. Only a few algorithms for finding acyclic edge colourings have been known by now. Moreover, these algorithms work only for graphs from particular classes. In our paper, we prove that @ga^'(G)=<(t-1)@D(G)+p for every graph G which satisfies the condition that |E(G^')|==2 is a given integer, the constant p=2t^3-3t+2. Based on that result, we obtain a polynomial algorithm which computes such a colouring. The class of graphs covered by our theorem is quite rich, for example, it contains all t-degenerate graphs." @default.
- W2000814123 created "2016-06-24" @default.
- W2000814123 creator A5081235427 @default.
- W2000814123 date "2011-02-01" @default.
- W2000814123 modified "2023-09-23" @default.
- W2000814123 title "Acyclic edge colourings of graphs with the number of edges linearly bounded by the number of vertices" @default.
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- W2000814123 doi "https://doi.org/10.1016/j.ipl.2010.12.002" @default.
- W2000814123 hasPublicationYear "2011" @default.
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