Abstract
We present the first linear time algorithm for d-list colouring of a graph—i.e. a proper colouring of each vertex v by colours coming from lists \(\mathcal{L}(v)\) of sizes at least deg(v). Previously, procedures with such complexity were only known for Δ-list colouring, where for each vertex v one has \(|\mathcal{L}(v)|\geq\Delta\), the maximum of the vertex degrees. An implementation of the procedure is available.
Partially supported by RFBR grant 09-01-12137-ofi_m, the president of Russia grant “Leading Scientific Schools” NSh-4392.2008.1.
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Gravin, N. (2010). Time Optimal d-List Colouring of a Graph. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_15
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DOI: https://doi.org/10.1007/978-3-642-13182-0_15
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