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A334303 Numbers m such that the Thue chromatic number of graph C_m is equal to 4. 0


%S 5,7,9,10,11,14,17

%N Numbers m such that the Thue chromatic number of graph C_m is equal to 4.

%C The Thue chromatic number of a graph G is the least number k such that there is a nonrepetitive coloring of length k, and no such coloring exists of length < k. (A coloring is nonrepetitive iff there is no path of even length such that the colors in the first half are in the same sequence as the colors in the second half.)

%C The Thue chromatic number of C_m for any other m > 2 is equal to 3.

%H J. D. Currie, <a href="https://doi.org/10.37236/1671">There are ternary circular square-free words of length n for n >= 18</a>, Elect. J. Combinatorics 9 (2002), Note #N10, 7 pp.

%H J. Grytczuk, <a href="https://doi.org/10.1155/2007/74639">Nonrepetitive colorings of graphs - a survey</a>, Int. J. Math. Math. Sci. (2007), Art. ID 74639, 10 pp.

%e 5 is in the sequence because at least four colors are needed to make an non-repetitive coloring of C_5.

%K nonn,fini,full

%O 1,1

%A _Bartlomiej Pawlik_, Apr 22 2020

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Last modified August 4 03:57 EDT 2021. Contains 346442 sequences. (Running on oeis4.)