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On the strong parity chromatic number

Július Czap; Stanislav Jendroľ; František Kardoš

Discussiones Mathematicae Graph Theory (2011)

  • Volume: 31, Issue: 3, page 587-600
  • ISSN: 2083-5892

Abstract

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A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.

How to cite

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Július Czap, Stanislav Jendroľ, and František Kardoš. "On the strong parity chromatic number." Discussiones Mathematicae Graph Theory 31.3 (2011): 587-600. <http://eudml.org/doc/271057>.

@article{JúliusCzap2011,
abstract = {A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.},
author = {Július Czap, Stanislav Jendroľ, František Kardoš},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {plane graph; k-planar graph; vertex colouring; strong parity vertex colouring; -planar graph},
language = {eng},
number = {3},
pages = {587-600},
title = {On the strong parity chromatic number},
url = {http://eudml.org/doc/271057},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Július Czap
AU - Stanislav Jendroľ
AU - František Kardoš
TI - On the strong parity chromatic number
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 3
SP - 587
EP - 600
AB - A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.
LA - eng
KW - plane graph; k-planar graph; vertex colouring; strong parity vertex colouring; -planar graph
UR - http://eudml.org/doc/271057
ER -

References

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  2. [2] O.V. Borodin, Solution of Ringel's problems on vertex-free coloring of plane graphs and coloring of 1-planar graphs,, Met. Diskret. Anal. 41 (1984) 12-26 (in Russian). Zbl0565.05027
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  8. [8] J. Czap, S. Jendroľ and F. Kardoš, Facial parity edge colouring, Ars Math. Contemporanea 4 (2011) 255-269. 
  9. [9] J. Czap, S. Jendroľ and M. Voigt, Parity vertex colouring of plane graphs, Discrete Math. 311 (2011) 512-520, doi: 10.1016/j.disc.2010.12.008. Zbl1222.05051
  10. [10] H. Enomoto and M. Hornák, A general upper bound for the cyclic chromatic number of 3-connected plane graphs, J. Graph Theory 62 (2009) 1-25, doi: 10.1002/jgt.20383. Zbl1190.05052
  11. [11] H. Enomoto, M. Hornák and S. Jendroľ, Cyclic chromatic number of 3-connected plane graphs, SIAM J. Discrete Math. 14 (2001) 121-137, doi: 10.1137/S0895480198346150. Zbl0960.05048
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  13. [13] T. Kaiser, O. Ruck'y, M. Stehl'ik and R. Skrekovski, Strong parity vertex coloring of plane graphs, IMFM, Preprint series 49 (2011), 1144. 
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