Acute triangles in 4-connected maximal plane graphs

Ken Ichi Kawarabayashi, Atsuhiro Nakamoto, Yoshiaki Oda, Mamoru Watanabe

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we show that every 4-connected maximal plane graph with m finite faces other than the octahedron can be drawn in the plane so that at least (m+3)/2 faces are acute triangles. Moreover, this bound is sharp.

Original languageEnglish
Pages (from-to)95-106
Number of pages12
JournalDiscrete Mathematics
Volume292
Issue number1-3
DOIs
Publication statusPublished - 2005 Mar 28

Fingerprint

Acute triangle
Plane Graph
Face
Octahedron

Keywords

  • 4-Connected maximal plane graphs
  • Acute triangles
  • Contractions
  • Straight-line embeddings

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Acute triangles in 4-connected maximal plane graphs. / Kawarabayashi, Ken Ichi; Nakamoto, Atsuhiro; Oda, Yoshiaki; Watanabe, Mamoru.

In: Discrete Mathematics, Vol. 292, No. 1-3, 28.03.2005, p. 95-106.

Research output: Contribution to journalArticle

Kawarabayashi, KI, Nakamoto, A, Oda, Y & Watanabe, M 2005, 'Acute triangles in 4-connected maximal plane graphs', Discrete Mathematics, vol. 292, no. 1-3, pp. 95-106. https://doi.org/10.1016/j.disc.2004.09.008
Kawarabayashi, Ken Ichi ; Nakamoto, Atsuhiro ; Oda, Yoshiaki ; Watanabe, Mamoru. / Acute triangles in 4-connected maximal plane graphs. In: Discrete Mathematics. 2005 ; Vol. 292, No. 1-3. pp. 95-106.
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