Frugal Colouring of Graphs
Discrete Mathematics
2007-05-23 v1 Networking and Internet Architecture
Abstract
A -frugal colouring of a graph is a proper colouring of the vertices of such that no colour appears more than 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 -labelling. We also study frugal edge-colourings of multigraphs.
Cite
@article{arxiv.0705.0422,
title = {Frugal Colouring of Graphs},
author = {Omid Amini and Louis Esperet and Jan Van Den Heuvel},
journal= {arXiv preprint arXiv:0705.0422},
year = {2007}
}