This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381562 #4 Feb 28 2025 12:04:30
%S A381562 6,8,9,9,8,8,8,8,8,8,8,7,8,8,8,7
%N A381562 Minimum 2-tone chromatic number of maximal planar graphs with n vertices.
%C A381562 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.
%C A381562 For n in {19,22,23,27}, a(n) is either 7 or 8. All larger values are 7.
%H A381562 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/2tonejcpaper.pdf">2-Tone coloring of joins and products of graphs</a>, Congr. Numer. 217 (2013) 171-190.
%H A381562 Allan Bickle, <a href="https://bica.the-ica.org/Volumes/103//Reprints/BICA2023-46-Reprint.pdf">2-Tone Coloring of Planar Graphs</a>, Bull. Inst. Combin. Appl. 103 (2025) 114-129.
%H A381562 Allan Bickle and B. Phillips, <a href="https://allanbickle.files.wordpress.com/2016/05/ttonepaperb.pdf">t-Tone Colorings of Graphs</a>, Utilitas Math, 106 (2018) 85-102.
%F A381562 a(n) = 7 for n > 27.
%e A381562 For n=3, all 3 vertices get two distinct colors, so a(3) = 6.
%e A381562 For n=4, all 4 vertices get two distinct colors, so a(3) = 8.
%e A381562 For n=5 or 6, the extremal graph is a double wheel.
%Y A381562 Cf. A003057, A351120 (pair coloring).
%Y A381562 Cf. A350361 (trees), A350362 (cycles), A350715 (wheels), A366727 (outerplanar), A366728 (square of cycles).
%K A381562 nonn
%O A381562 3,1
%A A381562 _Allan Bickle_, Feb 27 2025