Guillermo Pineda Villavicencio - Research
Current Research Project/Students
- Graph reconstruction of polytopes: This project is about reconstructing the combinatorial structure of a polytope from its graph or dual graph, and if a reconstruction is possible, how efficiently it can be performed. The combinatorial structure of polytopes is given by partially ordering the polytope faces by the inclusion relation.
- Degree-diameter problem: This project aims to prove existence or otherwise of large graphs subject to constraints to the maximum degree, diameter and the graph class. Graph classes of interest include Cayley graphs and graphs embedded on surfaces. Students: Associated Supervisor of a completed PhD thesis and of an ongoing PhD student: Both students have been enrolled at the University of Newcastle.
- Applications of Graph Theory to Sport Scheduling: This project applies graph theory concepts and methodology to sport scheduling.
- Students: Supervisor of an honours thesis.
Consulting and other activities
- Participant of the program "Mathematicians in Schools'", an initiative of the Australian Government Department of Education. The applicant brings theory and real-world applications of geometry and graph theory to secondary school teachers and students.
- Translator of the book "Topology without tears'' by Sid Morris from English into Spanish.
- Moderator and Contributor to the project Combinatorics Wiki (combinatoricswiki.org), project aiming to present the latest concepts, results, conjectures and references in various topics of Combinatorics.
- *E. Nevo, G. Pineda-Villavicencio and D. R. Wood, On the maximum order of graphs embedded in surfaces, arxiv:1312.1753.
- G. Pineda-Villavicencio, Non-existence of bipartite graphs of diameter at least 4 and defect 2, Journal of Algebraic Combinatorics 34 (2011), no. 2, 163-182.
- C. Delorme and G. Pineda-Villavicencio, On graphs with cyclic defect or excess, The Electronic Journal of Combinatorics 17 (2010), no. 1, R143.
- E. Loz and G. Pineda-Villavicencio, New benchmarks for large scale networks with given maximum degree and diameter, The Computer Journal 53 (2010), no. 7, 1092-1105.
- C. Delorme, L. K. J¿¿rgensen, M. Miller and G. Pineda-Villavicencio, On bipartite graphs of diameter 3 and defect 2, Journal of Graph Theory 61 (2009), no. 4, 271-288.
Professional Memberships and Associations
- International Institute of Combinatorics and Its Applications (ICA) (since 2006).
- Accredited Member (MAustMS) of the Australian Mathematical Society (since 2009).
- Combinatorial Mathematics Society of Australasia Inc. (CMSA) (since 2009).
- American Mathematical Society (since 2010).
- Mathematical Association of America (since 2010).
I research on the theory and application of Discrete Mathematics. I am mainly interested in the areas of Combinatorial Optimisation, Discrete Geometry and Graph Theory.