Nonrepetitive Graph Colouring

Notes on Nonrepetitive Graph Colouring

A vertex colouring of a graph is nonrepetitive on paths if there is no path v1, v2, . . . , v2t such that vi and vt+i receive the same colour for all i = 1, 2, . . . , t. We determine the maximum density of a graph that admits a k-colouring that is nonrepetitive on paths. We prove that every graph has a subdivision that admits a 4-colouring that is nonrepetitive on paths. The best previous boun...

Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is nonrepetitive if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively l-choosable if given lists of at least l colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that, for some constant c, every graph with maximum degree ∆ is...

New Bounds for Facial Nonrepetitive Colouring

We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and of any planar graph is at most 22.

Colouring a Graph Frugally

Evolutionary Graph Colouring

The problem we are addressing in this paper was proposed at SIROCCO’98 by Kranakis [1], with possible applications to finding a consensus in distributive networks. The problem can be viewed as a simple game on graphs, in a way similar to the game of life. The aim is to colour all vertices of a graph, which are initially coloured with three colours 0,1, and 2, with a single colour. The only rule...