login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A350362 2-tone chromatic number of an n-cycle. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

The 2-tone 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 2-tone 5-coloring 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, t-Tone Colorings of Graphs, Utilitas Math, 106 (2018) 85-102.

Allan Bickle, 2-Tone coloring of joins and products of graphs, Congr. Numer. 217 (2013), 171-190.

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.

-12-34-56-

-12-34-15-36-

-12-34-51-23-45-

-12-34-15-32-14-35-

-12-34-56-13-24-35-46-

-12-34-15-23-14-25-13-45-

-12-34-15-32-14-25-13-24-35-

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 05:38 EST 2022. Contains 358431 sequences. (Running on oeis4.)