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Acute triangulations of convex quadrilaterals. (English) Zbl 1250.52001

An acute triangulation of a polygon \(P\) is a triangulation of \(P\) into acute triangles. Let \(f(P)\) be the minimum number of triangles necessary for an acute triangulation of \(P\).
Solving a problem raised by H. Maehara [Lect. Notes Comput. Sci. 2098, 237–243 (2001; Zbl 0998.52005)], the author proves that the maximum value of \(f(Q)\) for all convex quadrilaterals \(Q\) is equal to 8.

MSC:

52A10 Convex sets in \(2\) dimensions (including convex curves)
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
05C10 Planar graphs; geometric and topological aspects of graph theory

Citations:

Zbl 0998.52005
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References:

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