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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1518,
author = {Geir Agnarsson and Magn\'us M. Halld\'orsson},
title = {Vertex coloring the square of outerplanar graphs of low degree},
journal = {Discussiones Mathematicae Graph Theory},
volume = {30},
year = {2010},
pages = {619-636},
zbl = {1217.05056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1518}
}
Geir Agnarsson; Magnús M. Halldórsson. Vertex coloring the square of outerplanar graphs of low degree. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 619-636. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1518/
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