ArticleOriginal scientific text
Title
Vertex coloring the square of outerplanar graphs of low degree
Authors 1, 2
Affiliations
- Department of Mathematical Sciences, George Mason University, MS 3F2, 4400 University Drive, Fairfax, VA 22030, USA
- Department of Computer Science, Reykjavík University, IS-103 Reykjavík, Iceland
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
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Pages:
619-636
Main language of publication
English
Received
2009-07-31
Accepted
2010-01-11
Published
2010
DOI: 10.7151/dmgt.1518
Exact and natural sciences