Anagram-Free Graph Colouring

Anagram-free colourings of graph subdivisions

An anagram is a word of the form WP where W is a non-empty word and P is a permutation of W . A vertex colouring of a graph is anagram-free if no subpath of the graph is an anagram. Anagram-free graph colouring was independently introduced by Kamčev, Łuczak and Sudakov and ourselves. In this paper we introduce the study of anagram-free colourings of graph subdivisions. We show that every graph ...

Anagram-free colorings of graphs

A sequence S is called anagram-free if it contains no consecutive symbols r1r2 . . . rkrk+1 . . . r2k such that rk+1 . . . r2k is a permutation of the block r1r2 . . . rk. Answering a question of Erdős and Brown, Keränen constructed an infinite anagram-free sequence on four symbols. Motivated by the work of Alon, Grytczuk, Ha luszczak and Riordan [2], we consider a natural generalisation of ana...

List-colouring the square of a K4-minor-free graph

Let G be a K4-minor-free graph with maximum degree . It is known that if ∈ {2, 3} then G2 is ( + 2)-degenerate, so that (G2) ch(G2) + 3. It is also known that if 4 then G2 is ( 3 2 + 1)-degenerate and (G2) 3 2 + 1. It is proved here that if 4 then G2 is 3 2 -degenerate and ch(G2) 3 2 + 1. These results are sharp. © 2007 Elsevier B.V. All rights reserved.

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...