Guillermo Pineda-Villavicencio

Publications

Books
  1. G. Pineda-Villavicencio,  Polytopes and graphs, vol. 211,  Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2024.

A copy of the book is available for personal use from Deakin Research Online. Updates on the book are available here.

Preprints
  1. G. Pineda-Villavicencio, A. Tritama and D. Yost, A lower bound for d-polytopes with 2d+2 vertices, 27 pages, arXiv.
  2. G. Pineda-Villavicencio, J. Wang and D. Yost, Polytopes with low excess degree, 23 pages, arXiv.
  3. G. Pineda-Villavicencio, Cycle space of graphs of polytopes, 4 pages, arXiv. Note: This paper will not be sent to a journal, as this proof seems to be known to experts in the field.
  4. H. T. Bui, G. Pineda-Villavicencio and J. Ugon, The linkedness of cubical polytopes, 39 pages, arXiv
    Note: This paper was divided into two shorter papers: The linkedness of cubical polytopes: The cube and The linkedness of cubical polytopes: Beyond the cube.
    .
Refereed publications
  1. H. T. Bui, G. Pineda-Villavicencio and J. Ugon, The linkedness of cubical polytopes: Beyond the cube Discrete Mathematics 347 (2024), Article 113801, arXiv
  2. V. Pilaud, G. Pineda-Villavicencio and J. Ugon, Edge connectivity of simplicial polytopes, European Journal of Combinatorics 113 (2023), Article 103752, arXiv.
  3. G. Pineda-Villavicencio and D. Yost, The lower bound theorem for d-polytopes with 2d + 1 vertices, 26 pages, SIAM Journal on Discrete Mathematics 36 (2022), 2920-2941, arXiv.
  4. G. Pineda-Villavicencio, J. Ugon and D. Yost, Minimum number of edges of polytopes with 2d + 2 vertices, The Electronic Journal of Combinatorics 29 (2022), P3.18, arXiv.
  5. G. Pineda-Villavicencio and B. Schröter, Reconstructibility of matroid polytopes, SIAM Journal on Discrete Mathematics 36 (2022), 490-508, arXiv.
  6. L. K. Jörgensen, G. Pineda-Villavicencio and J. Ugon, Linkedness of Cartesian products of complete graphs, Ars Mathematica Contemporanea 22 (2022), P2.09, arXiv.
  7. R. Esmaeilbeigi, V. Mak-Hau, G. Pineda-Villavicencio, and J. Ugon, Hydrogen bus route planning in regional Victoria. In Vervoort, R.W., Voinov, A.A., Evans, J.P. and Marshall, L. (eds) MODSIM2021, 24th International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, December 2021, pp. 757–763.
  8. S. James, K. Morgan, G. Pineda-Villavicencio, and L. Tubino, Covid-19 and education: Learning and teaching in a pandemic-constrained environment, Ch. X: Assessing Mathematics During COVID-19 Times, Informing Science Press, 2021.
  9. H. T. Bui, G. Pineda-Villavicencio and J. Ugon, The linkedness of cubical polytopes: The cube, The Electronic Journal of Combinatorics 28 (2021), P3.45, arXiv.
  10. G. Pineda-Villavicencio, A new proof of Balinski’s theorem on the connectivity of polytopes, Discrete Mathematics 344 (2021),  arXiv.
  11. D. M. Morales-Silva, R. Atchison, C. S. McPherson, G. Pineda-Villavicencio . Using radar plots for performance benchmarking at patient and hospital levels using an Australian orthopaedics dataset, Health Informatics Journal 26 (2020), 2119-2137, doi.
  12. H. T. Bui, G. Pineda-Villavicencio and J. Ugon, Connectivity of cubical polytopes, Journal of Combinatorial Theory, Series A 169 (2020), 105-126, doi, arXiv.
  13. G. Pineda-Villavicencio, J. Ugon and D. Yost, Polytopes close to being simple, Discrete & Computational Geometry 64 (2020), 200-215, doi, arXiv.
  14. E. Nevo, G. Pineda-Villavicencio, J. Ugon and D. Yost, Almost simplicial polytopes I. The lower and upper bound theorems, Canadian Journal of Mathematics 72(2) (2020), 537-556, doi.
  15. G. Pineda-Villavicencio, J. Ugon and D. Yost, Lower bound theorems for general polytopes, European Journal of Combinatorics 79 (2019), 27-45, doi, arXiv.
  16. J. Doolittle, E. Nevo, G. Pineda-Villavicencio, J. Ugon and D. Yost, On the reconstruction of polytopes, Discrete & Computational Geometry 61(2) (2019), 285-302, doi, arXiv.
  17. G. Pineda-Villavicencio, J. Ugon and D. Yost, The excess degree of a polytope, SIAM Journal on Discrete Mathematics 32 (2018), 2011-2046, doi, arXiv.
  18. E. Nevo, G. Pineda-Villavicencio, J. Ugon and D. Yost, Almost simplicial polytopes: The lower and upper bound theorems, Proceedings of the 28th International Conference on Formal Power Series and Algebraic Combinatorics (Vancouver, British Columbia, Canada), Jul 2016. DMTCS Proceedings, 2016, 947-958. (Extended Abstract).
  19. E. Nevo, G. Pineda-Villavicencio and D. R. Wood, On the maximum order of graphs embedded in surfaces, Journal of Combinatorial Theory, Series B 119 (2016), 28-41, arXiv.
  20. G. Pineda-Villavicencio and D. R. Wood, The degree-diameter problem for sparse graph classes, The Electronic Journal of Combinatorics 22 (2015), no. 2, P2.46.
  21. C. Delorme and G. Pineda-Villavicencio, Quadratic form representations via generalized continuants, Journal of Integer Sequences 18 (2015), Article 15.6.4, arXiv.
  22. C. Delorme and G. Pineda-Villavicencio, Continuants and some decompositions into squares, Integers 15 (2015), paper A3, arXiv.
  23. R. Feria-Puron and G. Pineda-Villavicencio, Constructions of large graphs on surfaces, Graphs and Combinatorics 30 (2014), no. 4, 895-908, arXiv.
  24. G. Aloupis, H. Perez-Roses, G. Pineda-Villavicencio, P. Taslakian and D. Trinchet-Almaguer Fitting Voronoi Diagrams to Planar Tesselations, Lecture Notes in Computer Science 8288 (2013), 349-361, arXiv.
  25. R. Feria-Puron, M. Miller and G. Pineda-Villavicencio, On large bipartite graphs of diameter 3, Discrete Mathematics 313 (2013), no. 4, 381-390, arXiv.
  26. A. Dekker, H. Perez-Roses, G. Pineda-Villavicencio and P. Watters, The maximum degree & diameter-bounded subgraph and its applications, Journal of Mathematical Modelling and Algorithms 11 (2012), no. 3, 249-268.
  27. R. Feria-Puron and G. Pineda-Villavicencio, On bipartite graphs of defect at most 4, Discrete Applied Mathematics 160 (2012), 140-154, arXiv.
  28. R. Feria-Puron, M. Miller and G. Pineda-Villavicencio, On graphs of defect at most 2, Discrete Applied Mathematics 159 (2011), no. 13, 1331-1344, arXiv.
  29. 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.
  30. C. Delorme and G. Pineda-Villavicencio, On graphs with cyclic defect or excess, The Electronic Journal of Combinatorics 17 (2010), no. 1, R143.
  31. 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.
  32. G. Pineda-Villavicencio, Topology of interconnection networks with given degree and diameter (PhD Thesis Abstract), Bulletin of the Australian Mathematical Society 81 (2010), no. 2, 350-352.
  33. M. Miller and G. Pineda-Villavicencio, Complete catalogue of graphs of maximum degree 3 and defect at most 4, Discrete Applied Mathematics 157 (2009), no. 13, 2983-2996.
  34. M. Miller, M. Nguyen and G. Pineda-Villavicencio, On the nonexistence of graphs of diameter 2 and defect 2, Journal of Combinatorial Mathematics and Combinatorial Computing 71 (2009), 5-20.
  35. C. Delorme, L. K. Jorgensen, 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.
  36. C. Delorme, L. K. Jorgensen, M. Miller and G. Pineda-Villavicencio, On bipartite graphs of defect 2, European Journal of Combinatorics 30 (2009), no. 4, 798-808.
  37. G. Pineda-Villavicencio, J. Gomez, M. Miller and H. Perez-Roses, New largest known graphs of diameter 6, Networks 53 (2009), no. 4, 315-328.
  38. G. Pineda-Villavicencio and M. Miller. On graphs of maximum degree 3 and defect 4, Journal of Combinatorial Mathematics and Combinatorial Computing 65 (2008), 25-31.
  39. M. Miller, M. Nguyen and G. Pineda-Villavicencio. On the non-existence of even degree graphs of diameter 2 and defect 2. In: J. Harland and P. Manyem (editors), Proceedings of CATS 2008, the 14th Computing: The Australian Theory Symposium (CATS 2008), University of Wollongong, Australia, January 22-25, 2008. Australia. Conferences in Research and Practice in Information Technology.
  40. M. Nguyen, M. Miller and G. Pineda-Villavicencio. On the non-existence of odd degree graphs of diameter 2 and defect 2. In: L. Brankovic, Y.Q. Lin and W. F. Smyth (editors), Proceedings of IWOCA 2007, the Eighteenth International Workshop on Combinatorial Algorithms, 5-9 November, 2007, Lake Macquarie, N.S.W., pages 143-150. U.K. College Publications.
  41. G. Pineda Villavicencio and M. Miller. On Graphs of Maximum Degree 5, Diameter D and Defect 2. Proceedings of MEMICS 2006, 2nd Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, Mikulov, Czech Republic, 27-29 October, 2006.
  42. G. Pineda-Villavicencio, J. Gomez, M. Miller and H. Perez-Roses. New largest graphs of diameter 6. Electronic Notes in Discrete mathematics 24 (2006), 153-160.
  43. M. Miller and G. Pineda-Villavicencio, On Large Graphs with Given Degree and Diameter, Proceedings of AWOCA 2005, the Sixteenth Australasian Workshop on Combinatorial Algorithms, Ballarat, Australia, 18-21 September, 2005. p. 239-247, ISBN:0-646-45252-5.
  44. H. Perez-Roses, C. Cruz-Reyes, A. Martinez-Arias, J. Martinez-Mojicar and G. Pineda-Villavicencio. Different approaches to Voronoi Image Compression. Proceedings of XII CLAIO, the 12th Latin-Iberoamerican Operations Research Conference, Havana, Cuba, 2004, ISBN 959-261-166-1.
  45. R. M. Danger-Mercaderes, G. Pineda-Villavicencio and L. Valcarcel-Martinez. Module for Implementation of Geographic Information Systems. Proceedings of AUT 2002, the 2nd International Conference on Automatic Control, Santiago de Cuba, Cuba, July, 2002. Legal Deposit : B-35.469-02. ISBN: 84-699-9025-X.