Time optimal d-list colouring of a graph

Authors:
Nick Gravin
Affiliations:
St.Petersburg Department of Steklov Mathematical Institute RAS, Nanyang Technological University of Singapore
Venue:
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Year:
2010

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Δ-List vertex coloring in linear time

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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.