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

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

Offset

1,1

Comments

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.)

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

Links

Table of n, a(n) for n=1..7.

J. D. Currie, There are ternary circular square-free words of length n for n >= 18, Elect. J. Combinatorics 9 (2002), Note #N10, 7 pp.

J. Grytczuk, Nonrepetitive colorings of graphs - a survey, Int. J. Math. Math. Sci. (2007), Art. ID 74639, 10 pp.

Example

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

Crossrefs

Sequence in context: A275718 A129270 A153031 * A184110 A138892 A190202

Adjacent sequences: A334300 A334301 A334302 * A334304 A334305 A334306

Keyword

nonn,fini,full

Author

Bartlomiej Pawlik, Apr 22 2020

Status

approved