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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

COMMENTS

Best known upper bound is 5*n/3 + 78, established by Molloy and Salavatipour.

REFERENCES

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

G. Wegner, Graphs with given diameter and a coloring problem, preprint, University of Dortmund, 1977 [cited by Lih and Wang as source of conjecture].

LINKS

Table of n, a(n) for n=4..66.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = n + 5 if 4 <= n <= 7; 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

Adjacent sequences:  A121813 A121814 A121815 * A121817 A121818 A121819

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Aug 26 2006

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)