Triangulations without Minimum-Weight Drawing

Authors:
Cao An Wang;Francis Y. L. Chin;Bo-Ting Yang
Affiliations:
-;-;-
Venue:
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Year:
2000

Citing 14
Cited 0

Computational geometry: an introduction

Computational geometry: an introduction
Toughness and Delaunay triangulations

Discrete & Computational Geometry
Transitions in geometric minimum spanning trees (extended abstract)

SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Properties of some Euclidean proximity graphs

Pattern Recognition Letters
The realization problem for Euclidean minimum spanning trees is NP-hard

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computing a subgraph of the minimum weight triangulation

Computational Geometry: Theory and Applications
Algorithms for drawing graphs: an annotated bibliography

Computational Geometry: Theory and Applications
Drawing outerplanar minimum weight triangulations

Information Processing Letters
Maximum weight triangulation and graph drawing

Information Processing Letters
Graph Drawing: Algorithms for the Visualization of Graphs

Graph Drawing: Algorithms for the Visualization of Graphs
Drawable and Forbidden Minimum Weight Triangulations

GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Recognizing Rectangle of Influence Drawable Graphs

GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Proximity Drawability: a Survey

GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Proximity Constraints and Representable Trees

GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing

Quantified Score

Hi-index	0.00

Visualization

Abstract

It is known that some triangulation graphs admit straight-line drawings realizing certain characteristics, e.g., greedy triangulation, minimumweight 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.