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Coloring Eulerian Triangulations of the Klein Bottle

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Abstract

We show that an Eulerian triangulation of the Klein bottle has chromatic number equal to six if and only if it contains a complete graph of order six, and it is 5-colorable, otherwise. As a consequence of our proof, we derive that every Eulerian triangulation of the Klein bottle with face-width at least four is 5-colorable.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Institute for Theoretical Computer Science, Charles University, Malostranské náměstí 25, 118 00, Prague, Czech Republic

    Daniel Král’

  2. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Bojan Mohar

  3. Department of Mathematics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Bojan Mohar

  4. Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, 79-2 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan

    Atsuhiro Nakamoto

  5. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00, Prague, Czech Republic

    Ondřej Pangrác

  6. Tsuruoka National College of Technology, Tsuruoka, Yamagata, 997-8511, Japan

    Yusuke Suzuki

Authors
  1. Daniel Král’
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  2. Bojan Mohar
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  3. Atsuhiro Nakamoto
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  4. Ondřej Pangrác
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  5. Yusuke Suzuki
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Corresponding author

Correspondence to Daniel Král’.

Additional information

The Institute for Theoretical Computer Science (ITI) is supported by the Ministry of Education of the Czech Republic as project 1M0545. Daniel Král’ was supported by the Czech-Slovenian bilateral research project MEB091037. Ondřej Pangrác was supported by the grant GACR 201/09/0197.

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Král’, D., Mohar, B., Nakamoto, A. et al. Coloring Eulerian Triangulations of the Klein Bottle. Graphs and Combinatorics 28, 499–530 (2012). https://doi.org/10.1007/s00373-011-1063-9

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  • DOI: https://doi.org/10.1007/s00373-011-1063-9

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