Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2007-11

May 2007

Frugal Colouring of Graphs

Omid Amini, Louis Esperet, and Jan van den Heuvel

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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		Phone: +44(0)-20-7955 7494. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk