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.


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


Zbl 0998.52005
Full Text: DOI


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