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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

Improper colouring of (random) unit disk graphs

Abstract

For any graph $G$, the $k$-improper chromatic number $χ ^k(G)$ is the smallest number of colours used in a colouring of $G$ such that each colour class induces a subgraph of maximum degree $k$. We investigate the ratio of the $k$-improper chromatic number to the clique number for unit disk graphs and random unit disk graphs to extend results of [McRe99, McD03] (where they considered only proper colouring).
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Dates and versions

hal-01184358 , version 1 (14-08-2015)

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Ross J. Kang, Tobias Müller, Jean-Sébastien Sereni. Improper colouring of (random) unit disk graphs. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.193-198, ⟨10.46298/dmtcs.3402⟩. ⟨hal-01184358⟩
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