Acute triangles in 4-connected maximal plane graphs

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

doi:10.1016/j.disc.2004.09.008

Acute triangles in 4-connected maximal plane graphs

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	95-106
Number of pages	12
Journal	Discrete Mathematics
Volume	292
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.09.008
Publication status	Published - 2005 Mar 28

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2004.09.008

Cite this

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title = "Acute triangles in 4-connected maximal plane graphs",

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.",

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author = "Kawarabayashi, {Ken Ichi} and Atsuhiro Nakamoto and Yoshiaki Oda and Mamoru Watanabe",

year = "2005",

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AU - Kawarabayashi, Ken Ichi

AU - Nakamoto, Atsuhiro

AU - Oda, Yoshiaki

AU - Watanabe, Mamoru

PY - 2005/3/28

Y1 - 2005/3/28

N2 - 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.

AB - 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.

KW - 4-Connected maximal plane graphs

KW - Acute triangles

KW - Contractions

KW - Straight-line embeddings

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JF - Discrete Mathematics

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Acute triangles in 4-connected maximal plane graphs

Abstract

Keywords

ASJC Scopus subject areas

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