Faculty of Science and Technology

Discrete geometry and graph theory

Campus: Mt Helen

Discipline: Mathematics

Research field: Discrete Geometry and Graph Theory

Key words: polytopes, graphs

Supervisor(s): Dr Guillermo Pineda-Villavicencio

Contact details: Office T215

Email: g.pinedavillavicencio@federation.edu.au

Phone (optional)

Brief Supervisor Bio In 2002 I completed my Bachelor degree in Computer Science with first class honours at the University of Oriente (Cuba), and in 2009 my PhD in Mathematics at Federation University Australia (FedUni).

I currently research on the theory and application of Discrete Mathematics. Within Discrete Mathematics, I am mainly interested in the areas of Graph Theory and Discrete Geometry. However, I have also worked on Computational Geometry and on the design of geographic information systems.

The research group on Discrete Geometry at FedUni is formed by A/Prof David Yost, Dr Julien Ugon, Dr Ewan Barker and myself.  I also form part of the Centre for Informatics and Applied Optimization at FedUni.

For more details visit my webpage at federation.edu.au/guillermo

Project title: Topics on graphs of polytopes

Project Description

This project looks at traditional graph-theoretical problems in the context of graphs of polytopes. Polytopes are convex hulls of finitely many points in some Euclidean space, and their combinatorial structure is given by partially ordering the polytope faces by the inclusion relation. This project specifically deals with the combinatorics of polytopes.

In the past, we have looked at classifying polytopes with the smallest number of edges, and at graph reconstruction of polytopes; that is, at reconstructing the combinatorial structure of a polytope from its graph. And if a reconstruction is possible, we are also interested in how efficiently it can be performed.

Specific projects in this wide area will be tailored at the interest and mathematical background of the prospective student.