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# Frugal Colouring of 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 : A $k$-frugal colouring of a graph~$G$ is a proper colouring of the vertices of~$G$ such that no colour appears more than~$k$ times in the neighbourhood of a vertex. This type of colouring was introduced by Hind, Molloy and Reed in 1997. In this paper, we study the frugal chromatic number of planar graphs, planar graphs with large girth, and outerplanar graphs, and relate this parameter with several well-studied colourings, such as colouring of the square, cyclic colouring, and $L(p,q)$-labelling. We also study frugal edge-colourings of multigraphs.
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Cited literature [1 references]

https://hal.inria.fr/inria-00144318
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Thursday, May 3, 2007 - 10:11:28 AM
Last modification on : Monday, December 20, 2021 - 4:50:10 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:34:19 PM

### Files

RR-6178.pdf
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### Identifiers

• HAL Id : inria-00144318, version 2
• ARXIV : 0705.0422

### Citation

Omid Amini, Louis Esperet, Jan van den Heuvel. Frugal Colouring of Graphs. [Research Report] RR-6178, INRIA. 2007, pp.12. ⟨inria-00144318v2⟩

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