# Drawing Planar Graphs of Bounded Degree with Few Slopes

```@inproceedings{Keszegh2010DrawingPG,
title={Drawing Planar Graphs of Bounded Degree with Few Slopes},
author={Bal{\'a}zs Keszegh and J{\'a}nos Pach and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi},
booktitle={Graph Drawing},
year={2010}
}```
• Published in Graph Drawing 2010
• Mathematics, Computer Science
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… Expand
27 Citations
The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree
• Mathematics, Computer Science
• Graphs Comb.
• 2013
It is shown that the planar slope number of every planar partial 3-tree and also every plane partial 2-tree is at most O(Δ5), and the question of Dujmović et al. (Comput Geom 38(3):194–212, 2007) whether there is a function f such that plane maximal outerplanar graphs can be drawn using at most f( Δ) slopes is answered. Expand
Planar Drawings with Few Slopes of Halin Graphs and Nested Pseudotrees
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• 2021
This paper proves psn(G) ∈ Θ(∆) when G is a Halin graph, and thus has treewidth three, and presents the first polynomial upper bound on the planar slope number for a family of graphs havingtreewidth four, and shows that O(∅) slopes suffice for nested pseudotrees. Expand
Upward Planar Drawings with Three and More Slopes
• Computer Science
• 2021
It is shown that in general NP-hard to decide whether a given directed graph with maximum in and outdegree at most k admits such a drawing with k slopes, and for cactus graphs deciding and constructing a drawing can be done in polynomial time. Expand
Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles
• Mathematics, Computer Science
• Graph Drawing
• 2018
Lower bounds for the slope number of straight-line 1-planar drawings in terms of number of vertices and maximum degree are proved. Expand
Drawing Outer 1-planar Graphs with Few Slopes
• Mathematics, Computer Science
• Graph Drawing
• 2014
It is shown that an outer 1-planar graph G of bounded degree Δ admits an outer 3-line drawing that uses OΔ different slopes, which extends a previous result by Knauer et al. about the planar slope number of outerplanar graphs CGTA. Expand
Outerplanar Graph Drawings with Few Slopes
• Mathematics, Computer Science
• COCOON
• 2012
It is proved that Δ − 1 directions suffice for every outerplanar graph with maximum degree Δ ≥ 4, which improves the previous bound of O(Δ5), which was shown for planar partial 3-trees, a superclass of outerPlanar graphs. Expand
Planar Octilinear Drawings with One Bend Per Edge
• Mathematics, Computer Science
• Graph Drawing
• 2014
This paper proves that every 4-planar graph admits a planar octilinear drawing with at most one bend per edge on an integer grid of size On 2 ×On, and gives a class of graphs whose planarOctILinear drawings require at least two bends per edge. Expand
On the Total Number of Bends for Planar Octilinear Drawings
• Mathematics, Computer Science
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The first (non-trivial) upper bound on the required number of bends is derived from a result on the planar slope number of graphs by Keszegh et al. Expand
The Complexity of Bendless Three-Dimensional
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Contact Representations of Sparse Planar Graphs
It is shown that every plane ( 2, 2)-sparse graph has a CCA-representation, and that any plane (2, 1)-tight graph or (2 - 0)-tightgraph dual to a (2- 3)-tightGraph or (1, 4-tight graph) has aCCA- Representation; and that finding such a representation for a plane(2, 0)- Tight graph with maximum degree 5 is an NP-complete problem. Expand