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

Peterin, Iztok; Schreyer, Jens GND; Fecková Škrabul’áková, Erika; Taranenko, Andrej

A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2 · · · r2n such that ri = rn+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.

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