Vertex coloring the square of outerplanar graphs of low degree

Geir Agnarsson; Magnús M. Halldórsson

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 4, page 619-636
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Geir Agnarsson, and Magnús M. Halldórsson. "Vertex coloring the square of outerplanar graphs of low degree." Discussiones Mathematicae Graph Theory 30.4 (2010): 619-636. <http://eudml.org/doc/271020>.

@article{GeirAgnarsson2010,
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.},
author = {Geir Agnarsson, Magnús M. Halldórsson},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {outerplanar; chromatic number; power of a graph; weak dual},
language = {eng},
number = {4},
pages = {619-636},
title = {Vertex coloring the square of outerplanar graphs of low degree},
url = {http://eudml.org/doc/271020},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Geir Agnarsson
AU - Magnús M. Halldórsson
TI - Vertex coloring the square of outerplanar graphs of low degree
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 4
SP - 619
EP - 636
AB - 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.
LA - eng
KW - outerplanar; chromatic number; power of a graph; weak dual
UR - http://eudml.org/doc/271020
ER -

References

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