Plane graphs with straight edges whose bounded faces are acute triangles

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Abstract

Let $T_n$ denote a graph obtained as a triangulation of an $n$-gon in the plane. A cycle of $T_n$ is called an enclosing cycle if at least one vertex lies inside the cycle. In this paper it is proved that a triangulation $T_n$ admits a straight-line embedding in the plane whose bounded faces are all acute triangles if and only if $T_n$ has no enclosing cycle of length $\le 4$. Those $T_n$ that admit straight-line embeddings in the plane without obtuse triangles are also characterized.

Journal

  • Journal of Combinatorial Theory Series B

    Journal of Combinatorial Theory Series B 88(2), 237-245, 2003-07

    ACADEMIC PRESS INC ELSEVIER SCIENCE

Codes

  • NII Article ID (NAID)
    120001371782
  • NII NACSIS-CAT ID (NCID)
    AA00695859
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0095-8956
  • Data Source
    IR 
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