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On improper interval edge colourings

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Abstract

We study improper interval edge colourings, defined by the requirement that the edge colours around each vertex form an integer interval. For the corresponding chromatic invariant (being the maximum number of colours in such a colouring), we present upper and lower bounds and discuss their qualities; also, we determine its values and estimates for graphs of various families, like wheels, prisms or complete graphs. The study of this parameter was inspired by the interval colouring, introduced by Asratian, Kamalian (1987). The difference is that we relax the requirement on the original colouring to be proper.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Sciences, University of P. J. Šafárik, Jesenná, 5, 040 01, Košice, Slovak Republic

    Peter Hudák

  2. LaBRI, University of Bordeaux, 351, cours de la Libération, 33405, Talence, France

    František Kardoš

  3. Institute of Mathematics, Faculty of Sciences, University of P. J. Šafárik, Jesenná 5, 040 01, Košice, Slovak Republic

    Tomáš Madaras & Michaela Vrbjarová

Authors
  1. Peter Hudák
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  2. František Kardoš
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  3. Tomáš Madaras
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  4. Michaela Vrbjarová
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Corresponding author

Correspondence to Peter Hudák.

Additional information

This work was supported in part by French national agency for the promotion of higher education, international student services, and international mobility under the bilateral contract No. 31777QK, by Slovak Science and Technology Assistance Agency under the bilateral Slovak-French contracts Nos. APVV-SK-FR-2013-0028, VVGS-PF-2014-447, VVGS-2014-179 and VVGS-PF-2015-484. Also, this study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the “Investments for the future” Programme IdEx Bordeaux—CPU (ANR-10-IDEX-03-02).

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Hudák, P., Kardoš, F., Madaras, T. et al. On improper interval edge colourings. Czech Math J 66, 1119–1128 (2016). https://doi.org/10.1007/s10587-016-0313-7

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  • DOI: https://doi.org/10.1007/s10587-016-0313-7

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