Vertex coloring the square of outerplanar graphs of low degree

Geir Agnarsson, Magnús M. Halldórsson
<span title="">2010</span> <i title="Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora"> <a target="_blank" rel="noopener" href="" style="color: black;">Discussiones Mathematicae Graph Theory</a> </i> &nbsp;
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 ∆ = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree ∆ = 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 ∆.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.7151/dmgt.1518</a> <a target="_blank" rel="external noopener" href="">fatcat:nu2vdbfpmzh2pnogbbdiphgkdi</a> </span>
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