# MultiPlane Graph Embedding (2.5D Graph Embeddability)

### Summary

The mathematics of embeddings of graphs in three dimensions with constraints using a set of 2D planes, called MultiPlane or 2.5D representation.

### Supervisor(s)

### Research Location

### Program Type

Masters/PHD

### Synopsis

Graph Drawing is to construct good geometric representation of graphs in two and three dimensions. Although Graph Drawing has been extensively studied due to wide range of applications such as VLSI design, information systems, sociology, biology, networks, and software engineering, majority of research has been devoted to study representations of graphs in two dimensions.

This project will investigate a new MultiPlane framework, which draws graphs using a set of 2D planes, nicely arranged in three dimensions, and satisfying new aesthetic criteria derived from topology and graph theory.

More specifically, this project aims to study Multiplane embeddings from both mathematical and computational points of view: define new mathematical criteria for MultiPlane embeddings and establish lower/upper bounds; characterise MultiPlane graphs; determine the complexity of computing MultiPlane embeddings; and design algorithms for constructing MultiPlane embeddings. In particular, strong skills and research interests in mathematics, algorithms and theoretical computer science are required.

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### Keywords

algorithm, graph theory, graph drawing, Discrete mathematics, computational geometry, topology, knot theory, linear algebra, Visualization

### Opportunity ID

The opportunity ID for this research opportunity is: **1033**

### Other opportunities with Professor Seok-Hee Hong

- Drawing Algorithms for Almost Planar Graphs
- Algorithms for Drawing Non-Planar Graphs in Three Dimensions
- Scalable Visual Analytics
- Visualization and Analysis of Large and Complex Biological Networks and Social Networks
- 2.5D Graph Navigation and Interaction Techniques
- Drawing Algorithms for Almost Planar Graphs