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Discussiones Mathematicae Graph Theory 30(4) (2010)
619-636
DOI: https://doi.org/10.7151/dmgt.1518
VERTEX COLORING THE SQUARE OF OUTERPLANAR GRAPHS OF LOW DEGREE
|
Geir Agnarsson
Department of Mathematical Sciences | Magnús M. Halldórsson
Department of Computer Science |
Abstract
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.
2010 Mathematics Subject Classification: Primary: 05C05,
05C15; Secondary: 05C10.
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Received 31 July 2009
Revised 11 January 2010
Accepted 11 January 2010
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