Monotone Grid Drawings of Planar Graphs

  title={Monotone Grid Drawings of Planar Graphs},
  author={Md. Iqbal Hossain and Md. Saidur Rahman},
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… 

Strongly Monotone Drawings of Planar Graphs

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

  • Patrizio Angelini
  • Mathematics
    2015 6th International Conference on Information, Intelligence, Systems and Applications (IISA)
  • 2015

Monotone Drawings of 3-Connected Plane Graphs

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.

Nearly optimal monotone drawing of trees

  • Dayu HeXin He
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 2016

On Monotone Drawings of Trees

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

Good spanning trees in graph drawing

Optimal Monotone Drawings of Trees

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

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

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

  • K. MastakasA. Symvonis
  • Mathematics
    2015 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.



Straight-line monotone grid drawings of series-parallel graphs

It is shown that a series–parallel graph of n vertices has a straight-line planar monotone drawing on a grid of size O(n) × O( n2) and such a drawing can be found in linear time.

Monotone Drawings of Graphs with Fixed Embedding

It is proved that biconnected embedded planar graphs and outerplane graphs always admit planar monotone drawings, and the linear-time drawing algorithms for these two graph classes are described.

Monotone Drawings of Graphs

We study a new standard for visualizing graphs: A monotone drawing is a straight-line drawing such that, for every pair of vertices, there exists a path that monotonically increases with respect to

Upward Planar Drawings of Series-Parallel Digraphs with Maximum Degree Three

A linear-time algorithm is given to test the upward planarity of a series-parallel digraph G with maximum degree three and obtain an upward planar drawing of G if G admits one.

Algorithms for Plane Representations of Acyclic Digraphs

Planar Graph Drawing

The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs and is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry.

On monotone paths among obstacles with applications to planning assemblies

If all of the obstacles are convex, it is proved that there always exists a monotone path between any two points in the plane in the presence of polygonal obstacles.

Dividing a Graph into Triconnected Components

An algorithm for dividing a graph into triconnected components is presented and is both theoretically optimal to within a constant factor and efficient in practice.

A graph reading behavior: Geodesic-path tendency

The results show that in performing path search tasks, when eyes encounter a node that has more than one link, links that go toward the target node are more likely to be searched first, and graph reading performance can be significantly improved.

Graph Drawing: Algorithms for the Visualization of Graphs

  • Graph Drawing: Algorithms for the Visualization of Graphs
  • 1999