Geodesic
Vertex coloring the square of outerplanar graphs of low degree
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 619-636.

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Vertex colorings of the square of an outerplanar graph have received a lot of attention recently. In this article we prove that the chromatic number of the square of an outerplanar graph of maximum degree Δ = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree Δ ≠ 6 is known. Hence, this mentioned chromatic number of 7 is the last and only unknown upper bound of the chromatic number in terms of Δ.
Keywords: outerplanar, chromatic number, power of a graph, weak dual 
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Agnarsson, Geir; Halldórsson, Magnús. Vertex coloring the square of outerplanar graphs of low degree. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 619-636. http://geodesic.mathdoc.fr/item/DMGT_2010_30_4_a7/

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