On the Number of Acute Triangles in a Straight-Line Embedding of a Maximal Planar Graph
Copyright policy )On the Number of Acute Triangles in a Straight-Line Embedding of a Maximal Planar Graph
We show that any maximal planar graph with \(m\) triangles except the unbounded face can be transformed into a straight-line embedding in which at least \(\lceil m/3\rceil\) triangles are acute triangles. Moreover, we show that any maximal outer-planar graph can be transformed into a straight-line embedding in which all faces are acute triangles except the unbounded face. \(\copyright\) Academic Press.
- Kogakkan University Japan
- Kurashiki University of Science and the Arts Japan
- University of the Ryukyus Japan
- Kogakuin University Japan
Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, maximal planar graph, straight-line embedding, acute triangles, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science
Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, maximal planar graph, straight-line embedding, acute triangles, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science
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