Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Signed diagonal flips and the four color theorem
European Journal of Combinatorics - In memoriam François Jaeger
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Some Applications of Orderly Spanning Trees in Graph Drawing
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Optimal Area Algorithm for Planar Polyline Drawings
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Watermelon uniform random generation with applications
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Improved visibility representation of plane graphs
Computational Geometry: Theory and Applications
Visibility representation of plane graphs via canonical ordering tree
Information Processing Letters
Visibility representation of plane graphs via canonical ordering tree
Information Processing Letters
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
GD'07 Proceedings of the 15th international conference on Graph drawing
Improved floor-planning of graphs via adjacency-preserving transformations
Journal of Combinatorial Optimization
An application of well-orderly trees in graph drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Planar graphs, via well-orderly maps and trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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A realizer of a maximal plane graph is a set of three particular spanning trees. It has been used in several graph algorithms and particularly in graph drawing algorithms. We propose colored flips on realizers to generalize Wagner's theorem on maximal planar graphs to realizers. From this result, it is proved that 驴0 + 驴1 + 驴2 - 驴 = n - 1 where 驴i is the number of inner nodes in the tree Ti, 驴 is the number of three colored faces in the realizer and n is the number of vertices. As an application of this formula, we show that orderly spanning trees with at most 驴 2n+1-驴/3 驴 leaves can be computed in linear time.