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Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
Theoretical Computer Science
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STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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GD '95 Proceedings of the Symposium on Graph Drawing
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ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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GD'04 Proceedings of the 12th international conference on Graph Drawing
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WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
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WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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GD'06 Proceedings of the 14th international conference on Graph drawing
GD'07 Proceedings of the 15th international conference on Graph drawing
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Proceedings of the twenty-sixth annual symposium on Computational geometry
Improved floor-planning of graphs via adjacency-preserving transformations
Journal of Combinatorial Optimization
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We define and investigate a structure called transversal edge-partition related to triangulations without non empty triangles, which is equivalent to the regular edge labeling discovered by Kant and He. We study other properties of this structure and show that it gives rise to a new straight-line drawing algorithm for triangulations without non empty triangles, and more generally for 4-connected plane graphs with at least 4 border vertices. Taking uniformly at random such a triangulation with 4 border vertices and n vertices, the size of the grid is almost surely $\frac{11}{27}n \times \frac{11}{27}n$up to fluctuations of order $\sqrt{n}$, and the half-perimeter is bounded by n–1. The best previously known algorithms for straight-line drawing of such triangulations only guaranteed a grid of size $(\lceil n/2\rceil - 1)\times \lfloor n/2 \rfloor$. Hence, in comparison, the grid-size of our algorithm is reduced by a factor $\frac{5}{27}$, which can be explained thanks to a new bijection between ternary trees and triangulations of the 4-gon without non empty triangles.