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Bipartite Polyhedral Maps on Closed Surfaces are Distinguishing 3-Colorable with Few Exceptions

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Abstract

A map on a closed surface is said to be distinguishing k -colorable if it has a proper k-coloring such that no automorphism other than the identity map preserves the colors. We shall show that a polyhedral map with bipartite underlying graph is distinguishing 3-colorable if it has more than 18 vertices.

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Authors and Affiliations

  1. Faculty of Environment and Information Sciences, Yokohama National University, 79-2 Tokiwadai, Hodogaya-Ku, Yokohama, 240-8501, Japan

    Seiya Negami

  2. Colgate University, 13 Oak Drive, Hamilton, NY, 13346, USA

    Thomas W. Tucker

Authors
  1. Seiya Negami
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  2. Thomas W. Tucker
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Correspondence to Seiya Negami.

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Negami, S., Tucker, T.W. Bipartite Polyhedral Maps on Closed Surfaces are Distinguishing 3-Colorable with Few Exceptions. Graphs and Combinatorics 33, 1443–1450 (2017). https://doi.org/10.1007/s00373-017-1788-1

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  • DOI: https://doi.org/10.1007/s00373-017-1788-1

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