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Journal of Graph Algorithms and Applications, ISSN 1526-1719, 2014, Volume 18, Issue 2, pp. 233 - 252
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2014, Volume 28, Issue 3, pp. 1093 - 1101
Schnyder characterized planar graphs in terms of order dimension. The structures used for the proof have found many applications. Researchers also found... 
Planar maps | Segment contact representation | Dimension | Ordered set | Grid intersection graph | Planar graphs | CONVEX DRAWINGS | MATHEMATICS, APPLIED | planar graphs | REPRESENTATION | planar maps | segment contact representation | grid intersection graph | dimension | ordered set | GRAPHS | Theorems | Maps | Mathematical analysis | Proving | Set theory | Graphs | Machinery | Incidence
Journal Article
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 06/2016, Volume 206, pp. 48 - 55
An L-shape is the union of a horizontal and a vertical segment with a common endpoint. These come in four rotations: ▪, ▪,▪ and ▪. A k-bend path is a simple... 
Co-planar graphs | Planar 3-trees | [formula omitted]-bend [formula omitted]-graphs | Intersection graphs | Segment graphs | k-bend VPG-graphs | MATHEMATICS, APPLIED | NUMBER | REPRESENTATIONS | CLIQUE PROBLEM | PATHS | COPLANAR GRAPHS | Subdivisions | Horizontal | Planes | Images | Segments | Graphs | Complement | Graphical representations | Computer Science
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2017, Volume 57, Issue 2, pp. 257 - 280
Journal Article
Journal Article
Journal of Graph Algorithms and Applications, ISSN 1526-1719, 08/2015, Volume 19, Issue 1, pp. 467 - 505
Journal Article
Discrete Mathematics and Theoretical Computer Science, 07/2016, Volume 18, Issue 3
We study Markov chains for αα-orientations of plane graphs, these are orientations where the outdegree of each vertex is prescribed by the value of a given... 
Markov chains | Graphs | Chain mobility | Markov analysis | Orientation
Journal Article
Journal of Graph Algorithms and Applications, ISSN 1526-1719, 2015, Volume 19, Issue 3, pp. 817 - 849
Journal Article
Journal of Integer Sequences, 12/2014, Volume 18, Issue 1
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 9627, pp. 114 - 127
Conference Proceeding
Order, ISSN 0167-8094, 7/2018, Volume 35, Issue 2, pp. 363 - 391
We study subclasses of grid intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is... 
Mathematics | Order, Lattices, Ordered Algebraic Structures | Algebra | Order dimension | Grid intersection graphs | Discrete Mathematics | MATHEMATICS | NUMBER | PLANAR
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 08/2017, Volume 61, pp. 421 - 427
Representations of planar triangulations as contact graphs of geometric shapes have received quite some attention in recent years. The most prominent example... 
Contact representation | Schnyder wood | α-orientation | pentagon
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2015, Volume 31, Issue 4, pp. 927 - 939
Kelly showed that there exist planar posets of arbitrarily large dimension, and Streib and Trotter showed that the dimension of a poset with a planar cover... 
Cover graph | Comparability graph | Mathematics | Engineering Design | Dimension | Combinatorics | Outerplanar graph | 05C35 | 06A07 | MATHEMATICS | ORDER DIMENSION | Graphs
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 9801, pp. 441 - 453
Conference Proceeding
Electronic Journal of Combinatorics, ISSN 1077-8926, 02/2004, Volume 11, Issue 1 R
The set of all orientations of a planar graph with prescribed outdegrees carries the structure of a distributive lattice. This general theorem is proven in the... 
MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2011, Volume 46, Issue 3, pp. 405 - 416
Arrangements of lines and pseudolines are important and appealing objects for research in discrete and computational geometry. We show that there are at most... 
Computational Mathematics and Numerical Analysis | Enumeration | Pseudoline | Cutpath | Mathematics | Combinatorial geometry | Combinatorics | MATHEMATICS | LINEAR ORDERS | ACYCLIC SETS | COMPUTER SCIENCE, THEORY & METHODS | BRUHAT ORDERS | Geometry | Computational mathematics | Computational geometry | Positioning | Planes | Coding | Upper bounds | Ingredients | Counting
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2018, Volume 11159, pp. 203 - 215
Conference Proceeding
Computational Geometry: Theory and Applications, ISSN 0925-7721, 11/2013, Volume 46, Issue 9, pp. 1036 - 1041
In this note, we present a simple combinatorial factor 6 algorithm for approximating the minimum hitting set of a family R={R1,…,Rn} of axis-parallel... 
Packing and covering | Approximation algorithm | Transversals | MATHEMATICS | MATHEMATICS, APPLIED | PACKING | BOXES | SCHEMES | GRAPHS | Computational geometry | Construction | Algorithms | Approximation | Planes | Rectangles | Mathematical analysis | Combinatorial analysis
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 09/2018, Volume 25, Issue 3
Representations of planar triangulations as contact graphs of a set of internally disjoint homothetic triangles or of a set of internally disjoint homothetic... 
Pentagon | Contact representation | Planar triangulation | Schnyder wood | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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