A note on the Thue chromatic number of lexicographic produts of graphs

Abstract

A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r 1 r 2 • • • r 2n such that r i = r n+i for all 1 ≤ i ≤ n). Let G be a graph whose vertices are coloured. A colouring ϕ of the graph G is non-repetitive if the sequence of colours on every path in G is non-repetitive. The Thue chromatic number, denoted by π(G), is the minimum number of colours of a non-repetitive colouring of G.

Nonrepetitive Graph Colouring

“…Nonrepetitive colourings of graph products have been studied in [17,30,47,91,99,121]. Here we focus on strong products because doing so has applications to numerous graph classes, such as planar graphs (Section 5.1) and graphs excluding a minor (Section 5.3).…”