Abstract
It is known that some triangulation graphs admit straight-line drawings realizing certain characteristics, e.g., greedy triangulation, minimum- weight triangulation, Delaunay triangulation, etc.. Lenhart and Liotta [12] in their pioneering paper on “drawable” minimum-weight triangulations raised an open problem: ‘Does every triangulation graph whose skeleton is a forest admit a minimum-weight drawing?’ In this paper, we answer this problem by disproving it in the general case and even when the skeleton is restricted to a tree or, in particular, a star.
This work is supported by NSERC grant OPG0041629 and RGC grant HKU 541/96E.
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Wang, C.A., Chin, F.Y., Yang, B. (2000). Triangulations without Minimum-Weight Drawing. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds) Algorithms and Complexity. CIAC 2000. Lecture Notes in Computer Science, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46521-9_14
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DOI: https://doi.org/10.1007/3-540-46521-9_14
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