Note on coloring of double disk graphs

Jaka Kranjc (), Borut Lužar (), Martina Mockovčiaková () and Roman Soták ()

Journal of Global Optimization, 2014, vol. 60, issue 4, 793-799

Abstract: The coloring of disk graphs is motivated by the frequency assignment problem. In 1998, Malesińska et al. introduced double disk graphs as their generalization. They showed that the chromatic number of a double disk graph $$G$$ G is at most $$33\,\omega (G) - 35$$ 33 ω ( G ) - 35 , where $$\omega (G)$$ ω ( G ) denotes the size of a maximum clique in $$G$$ G . Du et al. improved the upper bound to $$31\,\omega (G) - 1$$ 31 ω ( G ) - 1 . In this paper we decrease the bound substantially; namely we show that the chromatic number of $$G$$ G is at most $$15\,\omega (G) - 14$$ 15 ω ( G ) - 14 . Copyright Springer Science+Business Media New York 2014

Keywords: Disk graph; Double disk graph; Frequency assignment problem; Chromatic number (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-014-0221-z

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