Nonrepetitively 3-Colorable Subdivisions of Graphs with a Logarithmic Number of Subdivisions per edge
We show that for every graph $G$ and every graph $H$ obtained by subdividing each edge of $G$ at least $\Omega(\log |V(G)|)$ times, $H$ is nonrepetitively 3-colorable. In fact, we show that $\Omega(\log \pi'(G))$ subdivisions per edge are enough, where $\pi'(G)$ is the nonrepetitive chromatic index of $G$. This answers a question of Wood and improves a similar result of Pezarski and Zmarz that stated the existence of at least one 3-colorable subdivision with a linear number of subdivision vertices per edge.
2020 ◽
Vol 932
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pp. 012059
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2007 ◽
Vol 307
(14)
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pp. 1767-1775
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2017 ◽
Vol 340
(5)
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pp. 1143-1149
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2000 ◽
Vol 17
(2)
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pp. 117-156
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