Abstract
The Grundy number of a graph G, denoted by \({\it \Gamma} (G)\), is the largest k such that G has a greedy k-colouring, that is a colouring with k colours obtained by applying the greedy algorithm according to some ordering of the vertices of G. Trivially \({\it \Gamma(G)\leq \Delta(G)+1}\). In this paper, we show that deciding if \({\it \Gamma(G)\leq \Delta(G)}\) is NP-complete. We then show that deciding if \({\it \Gamma(G)\geq \mid V(G)\mid-k}\) is fixed parameter tractable with respect to the parameter k.
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Havet, F., Sampaio, L. (2010). On the Grundy Number of a Graph. In: Raman, V., Saurabh, S. (eds) Parameterized and Exact Computation. IPEC 2010. Lecture Notes in Computer Science, vol 6478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17493-3_17
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DOI: https://doi.org/10.1007/978-3-642-17493-3_17
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