# Monotone Grid Drawings of Planar Graphs

@article{Hossain2014MonotoneGD, title={Monotone Grid Drawings of Planar Graphs}, author={Md. Iqbal Hossain and Md. Saidur Rahman}, journal={ArXiv}, year={2014}, volume={abs/1310.6084} }

A monotone drawing of a planar graph $G$ is a planar straight-line drawing of $G$ where a monotone path exists between every pair of vertices of $G$ in some direction. Recently monotone drawings of planar graphs have been proposed as a new standard for visualizing graphs. A monotone drawing of a planar graph is a monotone grid drawing if every vertex in the drawing is drawn on a grid point. In this paper we study monotone grid drawings of planar graphs in a variable embedding setting. We show…

## 13 Citations

### Strongly Monotone Drawings of Planar Graphs

- MathematicsSoCG
- 2016

This work presents algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graph, outerplanar graphs, and 2-trees, and their drawings are strictly convex.

### Monotone drawings of graphs with few directions

- Mathematics2015 6th International Conference on Information, Intelligence, Systems and Applications (IISA)
- 2015

### Monotone Drawings of 3-Connected Plane Graphs

- MathematicsESA
- 2015

This paper shows that the classical Schnyder drawing of 3-connected plane graphs is a monotone drawing on a grid of size f ×f (f ≤ 2n − 5 is the number of internal faces of G), which can be constructed in O(n) time.

### On Monotone Drawings of Trees

- MathematicsGraph Drawing
- 2014

It is shown how to construct a monotone drawing of a tree with n vertices on an On 1.5 ×On 1.

### Optimal Monotone Drawings of Trees

- MathematicsSIAM J. Discret. Math.
- 2017

An algorithm for constructing monotone drawings of trees on a grid of size at most 12n x 12n is presented, and the smaller drawing size is achieved by a new simple Path Draw algorithm, and a procedure that carefully assigns primitive vectors to the paths of the input tree T.

### Compact Monotone Drawing of Trees

- MathematicsCOCOON
- 2015

A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u, w in G, there exists a path \(P_{uw}\) in G that is monotone in some direction l. (Namely, the…

### Monotone Simultaneous Embeddings of Upward Planar Digraphs

- MathematicsJ. Graph Algorithms Appl.
- 2015

It is proved that if a monotone simultaneous embedding of three paths exists then it also exists for any possible choice of directions of monotonicity, and a polynomial-time algorithm is provided that, given three paths, decides whether amonotone simultaneously embedding exists and, in the case of existence, also constructs such an embedding.

### On the construction of increasing-chord graphs on convex point sets

- Mathematics2015 6th International Conference on Information, Intelligence, Systems and Applications (IISA)
- 2015

It is shown that given a convex point set P in the plane the authors can construct an increasing-chord graph consisting of P, at most one Steiner point and at most 4|P| - 8 edges.

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