Geodesic
Improper colouring of (random) unit disk graphs
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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). 
@article{DMTCS_2005_special_250_a11,
     author = {Kang, Ross J. and M\"uller, Tobias and Sereni, Jean-S\'ebastien},
     title = {Improper colouring of (random) unit disk graphs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
     year = {2005},
     doi = {10.46298/dmtcs.3402},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3402/}
}
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%V DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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Kang, Ross J.; Müller, Tobias; Sereni, Jean-Sébastien. Improper colouring of (random) unit disk graphs. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3402. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3402/

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