The Grundy number of a graph G, denoted by (G), is the largest k such that G has a greedy k-colouring, that is a colouring with k colours obtained by applying the greedy algorithm ...
: In this paper, we study the number of tilings of the hyperbolic plane that can be constructed, starting from a single pentagonal tile, the only permitted transformations on the b...
A basic problem in the design of mobile telephone networks is to assign sets of radio frequency bands (colours) to transmitters (vertices) to avoid interference. Often the transmi...
It is proved that, if G is a K4-minor-free graph with maximum degree 3, then G is totally 4-choosable; that is, if every element (vertex or edge) of G is assigned a list of 4 colo...
A proper edge colouring of a graph is neighbour-distinguishing if for all pairs of adjacent vertices v, w the set of colours appearing on the edges incident with v is not equal to...
It is proved that edges of a graph G with no component K2 can be coloured using at most 2 log2 (G) + 1 colours so that any two adjacent vertices have distinct sets of colours of t...
Colour permeates our daily lives, yet we rarely take notice of it. In this work we utilise the SenseCam (a visual lifelogging tool), to investigte the predominant colours in one m...
Philip Kelly, Aiden R. Doherty, Alan F. Smeaton, C...
A graph with n vertices and maximum degree cannot be given weak sense of direction using less than colours. It is known that n colours are always sufficient, but it has been conje...
We survey a number of tools that have been developed for generating sets of colours according to commonly accepted rules for colour harmony. Informal manual techniques for generati...
In this paper we describe a technique for choosing multiple colours for use during data visualization. Our goal is a systematic method for maximizing the total number of colours a...