Vertex coloring the square of outerplanar graphs of low degree

• Autorzy: Geir Agnarsson , Magnús M. Halldórsson
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

outerplanar; chromatic number; power of a graph; weak dual

Kategorie tematyczne

• 05C05: Trees
• 05C15: Coloring of graphs and hypergraphs
• 05C10: Planar graphs; geometric and topological aspects of graph theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 4
• Strony: 619-636

Daty

wydano

2010

otrzymano

2009-07-31

poprawiono

2010-01-11

zaakceptowano

2010-01-11

Twórcy

autor

Geir Agnarsson

• Department of Mathematical Sciences, George Mason University, MS 3F2, 4400 University Drive, Fairfax, VA 22030, USA

autor

Magnús M. Halldórsson

• Department of Computer Science, Reykjavík University, IS-103 Reykjavík, Iceland

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1518