

A350362


2tone chromatic number of an ncycle.


3



6, 6, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
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OFFSET

3,1


COMMENTS

The 2tone chromatic number of a graph G is the smallest number of colors for which G has a coloring where every vertex has two distinct colors, no adjacent vertices have a common color, and no pair of vertices at distance 2 have two common colors.
There is no 2tone 5coloring for cycles of length 3, 4, or 7 since the Petersen graph does not contain cycles of these lengths.


LINKS

Table of n, a(n) for n=3..60.
Allan Bickle and B. Phillips, tTone Colorings of Graphs, Utilitas Math, 106 (2018) 85102.
Allan Bickle, 2Tone coloring of joins and products of graphs, Congr. Numer. 217 (2013), 171190.
N. Fonger, J. Goss, B. Phillips, and C. Segroves, Math 6450: Final Report, Group #2 Study Project, 2009.
Index entries for eventually constant sequences
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

a(n) = 5 for all n>7.
G.f.: x^3*(1 + x + x^4) + 5*x^3/(1  x).  Stefano Spezia, Dec 27 2021


EXAMPLE

The colorings for (broken) cycles with orders 3 through 9 are shown below.
123456
12341536
1234512345
123415321435
12345613243546
1234152314251345
123415321425132435
Colorings for larger cycles can be spliced together from broken cycles of lengths 5, 6, and 8.


CROSSREFS

Cf. A350361.
Sequence in context: A197478 A260713 A101801 * A351120 A199664 A019180
Adjacent sequences: A350359 A350360 A350361 * A350363 A350364 A350365


KEYWORD

nonn,easy


AUTHOR

Allan Bickle, Dec 26 2021


STATUS

approved



