# Improper colouring of (random) unit disk graphs

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : For any graph $G$, the $k$-improper chromatic number $\chi^k(G)$ 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 generalise results where only proper colouring was considered.
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https://hal.inria.fr/inria-00070259
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Submitted on : Friday, May 19, 2006 - 7:45:53 PM
Last modification on : Thursday, August 4, 2022 - 4:52:42 PM
Long-term archiving on: : Sunday, April 4, 2010 - 8:46:08 PM

### Identifiers

• HAL Id : inria-00070259, version 1

### Citation

Ross J. Kang, Tobias Müller, Jean-Sébastien Sereni. Improper colouring of (random) unit disk graphs. [Research Report] RR-5761, INRIA. 2005, pp.18. ⟨inria-00070259⟩

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