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<p>Dan Archdeacon raised an open problem: Does every triangulation of a surface by a complete graph have a Grünbaum coloring? In this paper, we partly solve this open problem of Dan Archdeacon by studying the triangular embeddings and Grünbaum coloring of the complete graphs <i>K</i><sub>12<i>s</i>+3</sub>, <i>K</i><sub>12<i>s</i>+4</sub> and <i>K</i><sub>12<i>s</i>+7</sub>.</p>

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Nonisomorphic Triangular Embeddings and Colorings of Complete Graphs

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Zhaoxiang Li,
  • Jiahong Liu

摘要

Dan Archdeacon raised an open problem: Does every triangulation of a surface by a complete graph have a Grünbaum coloring? In this paper, we partly solve this open problem of Dan Archdeacon by studying the triangular embeddings and Grünbaum coloring of the complete graphs K12s+3, K12s+4 and K12s+7.