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Cavicchioli, Maddalena

Acute triangulations of convex quadrilaterals. (English) Zbl 1250.52001

Discrete Appl. Math. 160, No. 7-8, 1253-1256 (2012).
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.
Reviewer: Anatoliy Milka (Kharkov)

Cited in 1 Document

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

Keywords:

acute triangulation; convex quadrilateral; planar straight-line graph

Citations:

Zbl 0998.52005
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\textit{M. Cavicchioli}, Discrete Appl. Math. 160, No. 7--8, 1253--1256 (2012; Zbl 1250.52001)
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References:

[1] Burago, Y.D.; Zalgaller, V.A., Polyhedral embedding of a net, Vestnik leningrad univ., 15, 66-80, (1960), (in Russian) · Zbl 0098.35403
[2] Cassidy, C.; Lord, G., A square acutely triangulated, J. recreat. math., 13, 263-268, (1980/81)
[3] Hangan, T.; Itoh, J.; Zamfirescu, T., Acute triangulations, Bull. math. soc. sci. math. roumanie, 43, (91) 3-4, 279-285, (2000) · Zbl 1048.51501
[4] Maehara, H., On acute triangulations of quadrilaterals, Discrete comput. geom., (2001), in: Proceedings of JCDCG 2000, Lect. Notes in Computer Science, vol. 2098, 2001, 237-354 · Zbl 0998.52005
[5] Manheimer, V., Solution to problem E1406: dissecting an obtuse triangle into acute triangles, Amer. math. monthly, 67, 923, (1960)
[6] Yuan, L., Acute triangulations of trapezoids, Discrete appl. math., 158, 1121-1125, (2010) · Zbl 1205.52006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.