Non-Repetitive 3-Coloring of Subdivided Graphs

Andrzej Pezarski, Michał Zmarz

Abstract


We show that every graph can be subdivided in a way that the resulting graph can be colored without repetitions on paths using only 3 colors. This extends the result of Thue asserting the existence of arbitrarily long nonrepetitive strings over a 3-letter alphabet.


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