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Note on coloring of double disk graphs

Author

Listed:
  • Jaka Kranjc
  • Borut Lužar
  • Martina Mockovčiaková
  • Roman Soták

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

Suggested Citation

  • Jaka Kranjc & Borut Lužar & Martina Mockovčiaková & Roman Soták, 2014. "Note on coloring of double disk graphs," Journal of Global Optimization, Springer, vol. 60(4), pages 793-799, December.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:4:p:793-799
    DOI: 10.1007/s10898-014-0221-z
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    References listed on IDEAS

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    1. Peeters, M.J.P., 1991. "On coloring j-unit sphere graphs," Other publications TiSEM 0678289b-1798-4adb-9ca1-9, Tilburg University, School of Economics and Management.
    2. Karen Aardal & Stan Hoesel & Arie Koster & Carlo Mannino & Antonio Sassano, 2007. "Models and solution techniques for frequency assignment problems," Annals of Operations Research, Springer, vol. 153(1), pages 79-129, September.
    3. Peeters, M.J.P., 1991. "On coloring j-unit sphere graphs," Research Memorandum FEW 512, Tilburg University, School of Economics and Management.
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