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A121816 Conjectured chromatic number of the square of an outerplanar graph G^2 as a function of the maximum degree of a vertex of G. 0
9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
LINKS
Ko-Wei Lih and Wei-Fan Wang, Coloring the Square of an Outerplanar Graph, Taiwanese Journal of Mathematics, Vol. 10, No. 4, 2006, pp. 1015-1023.
Michael Molloya and Mohammad R.Salavatipour, A bound on the chromatic number of the square of a planar graph, J. Combin. Theory Ser. B 94 (2005) 189-213.
G. Wegner, Graphs with given diameter and a coloring problem, University of Dortmund, 1977 [cited by Lih and Wang as source of conjecture].
FORMULA
a(n) = n + 5 if 4 <= n <= 7; a(n) = floor(3*n/2) + 1 if n >= 8.
a(n) = (3+(-1)^n+6*n)/4 for n>7. a(n) = a(n-1)+a(n-2)-a(n-3). G.f.: x^4*(x^6-8*x^2+x+9) / ((x-1)^2*(x+1)). - Colin Barker, Apr 30 2013
CROSSREFS
Sequence in context: A115843 A058365 A162789 * A196105 A196108 A181699
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Aug 26 2006
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)