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Colorability of Planar Graphs with Isolated Nontriangular Faces

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Abstract.

By a hole graph we mean a 2-connected planar graph where no two nontriangular faces have a vertex in common. We give necessary and sufficient conditions for a hole graph to be 3-colorable.

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Authors and Affiliations

  1. Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN, 37240-0001, USA

    Mark N. Ellingham

  2. Institute of Information Systems, Technical University of Vienna, Favoritenstrasse 9-11, A-1040, Vienna, Austria

    Herbert Fleischner

  3. MÚ SAV, Štefánikova 49, 814 73, Bratislava 1, Slovakia

    Martin Kochol

  4. Commission for Scientific Visualization, Austrian Academy of Sciences, Donau-City-Strasse 1, A-1220, Vienna, Austria

    Emanuel Wenger

Authors
  1. Mark N. Ellingham
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  2. Herbert Fleischner
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  3. Martin Kochol
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  4. Emanuel Wenger
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Corresponding author

Correspondence to Martin Kochol.

Additional information

Acknowledgments. This paper was prepared in framework of the exchange program between the Austrian and Slovak Academies of Sciences. The third author was active at Department of Mathematics, Vanderbilt University and Fakulta prírodných vied, Žilinská univerzita v Žiline.

Mathematics Subject Classification (1991): 05C15

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Ellingham, M., Fleischner, H., Kochol, M. et al. Colorability of Planar Graphs with Isolated Nontriangular Faces. Graphs and Combinatorics 20, 443–446 (2004). https://doi.org/10.1007/s00373-004-0574-z

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  • DOI: https://doi.org/10.1007/s00373-004-0574-z

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