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# Improper colouring of (random) unit disk graphs

2 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 $χ ^k(G)$ 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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Conference papers
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Cited literature [13 references]

https://hal.inria.fr/hal-01184358
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Submitted on : Friday, August 14, 2015 - 11:37:16 AM
Last modification on : Thursday, August 4, 2022 - 4:52:44 PM
Long-term archiving on: : Sunday, November 15, 2015 - 10:59:47 AM

### File

dmAE0138.pdf
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### Citation

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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