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Note on coloring of double disk graphs

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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 \(G\) is at most \(33\,\omega (G) - 35\), where \(\omega (G)\) denotes the size of a maximum clique in \(G\). Du et al. improved the upper bound to \(31\,\omega (G) - 1\). In this paper we decrease the bound substantially; namely we show that the chromatic number of \(G\) is at most \(15\,\omega (G) - 14\).

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Acknowledgments

This work is partially supported by ARRS Program P1-0383 and by Creative Core FISNM-3330-13-500033. Additionally, the third author was partially financed by the project NEXLIZ - CZ.1.07/2.3.00/30.0038, which is co-financed by the European Social Fund and the state budget of the Czech Republic, and the fourth author was supported in part by Slovak VEGA Grant No. 1/0652/12, by the Slovak Science and Technology Assistance Agency under the contract APVV-0023-10, and the Project implementation: University Science Park TECHNICOM for Innovation Applications Supported by Knowledge Technology, ITMS: 26220220182, supported by the Research & Development Operational Programme funded by the ERDF.

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Correspondence to Borut Lužar.

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Kranjc, J., Lužar, B., Mockovčiaková, M. et al. Note on coloring of double disk graphs. J Glob Optim 60, 793–799 (2014) doi:10.1007/s10898-014-0221-z

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Keywords

  • Disk graph
  • Double disk graph
  • Frequency assignment problem
  • Chromatic number