On the Angular Resolution of Planar Graphs
SIAM Journal on Discrete Mathematics
A better heuristic for orthogonal graph drawings
Computational Geometry: Theory and Applications
Planar Drawings and Angular Resolution: Algorithms and Bounds (Extended Abstract)
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
The geometric thickness of low degree graphs
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Graph drawings with few slopes
Computational Geometry: Theory and Applications
Drawings of planar graphs with few slopes and segments
Computational Geometry: Theory and Applications
Drawing cubic graphs with at most five slopes
Computational Geometry: Theory and Applications
Geometric representation of cubic graphs with four directions
Computational Geometry: Theory and Applications
Crossing number of toroidal graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
The planar slope number of planar partial 3-trees of bounded degree
GD'09 Proceedings of the 17th international conference on Graph Drawing
Drawing cubic graphs with the four basic slopes
GD'11 Proceedings of the 19th international conference on Graph Drawing
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We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different slopes. If we allow the edges to be represented by polygonal paths with one bend, then 2d slopes suffice. Allowing two bends per edge, every planar graph with maximum degree d ≥ 3 can be drawn using segments of at most ⌈d/2⌉ different slopes. There is only one exception: the graph formed by the edges of an octahedron is 4-regular, yet it requires 3 slopes. These bounds cannot be improved.