DR. Bernardo Abrego

Classes Fall 2016

Math 150A. Calculus I. MTuTh 12:30pm - 1:55 pm Chaparral Hall 5119.

Website (In Moodle)

Publications

• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, T. Hackl, J. Pammer, A. Pilz, P. Ramos, G. Salazar, and V. Vogtenhuber. All good drawings of small complete graphs. In Proc. 26th European Workshop on Computational Geometry (EuroCG’15), Ljubljana, Slovenia, March 15-18 (2015) 57-60.
• B. M. Ábrego, A. Dumitrescu, S. Fernández-Merchant, and C. D. Tóth. Computational Geometry Column 61. SIGACT News 46, 2 (June 2015), 65-77. http://doi.acm.org/10.1145/2789149.2789162
  
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and V. Vogtenhuber.  Non-Shellable Drawings of Kn with Few Crossings. In Proc. 26th Annual Canadian Conference on Computational Geometry CCCG 2014, Halifax, Nova Scotia, Canada (2014).
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. Shellable drawings and the cylindrical crossing number of Kn.Discrete and Computational Geometry 52 (2014), no. 4, 743–753.
• B.M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. More on the crossing number of Kn: Monotone drawings. Electronic Notes in Discrete Mathematics, 44:411-414, 2013. Special issue dedicated to LAGOS 2013.
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. The 2-page crossing number of Kn.   Discrete and Computational Geometry 49 (2013), no. 4, 747–777.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, H. Meijer, V. Sacristán, M. Saumell. Proximity graphs inside large weighted graphs. Networks 61 (2013), 29-39.
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, P. Ramos, and G. Salazar. The 2-page crossing number of Kn (Extended Abstract).  Proceedings of the ACM Symposium on Computational Geometry, June 17–20, 2012, Chapel Hill, North Carolina, USA. (2012) 397-403.
• B. M. Ábrego, S. Fernández-Merchant, and G. Salazar. The rectilinear crossing number of Kn: Closing in (or are we?). To appear in Thirty essays in geometric graph theory, J. Pach (Ed), Springer (2012).
• B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)-edges, crossings, and halving lines of geometric drawings of Kn. Discrete and Computational Geometry 48 (2012), 192-215.
• B. M. Ábrego, S. Fernández-Merchant, D. B. Roberts. On the maximum number of isosceles right triangles in a finite point set. Involve 4 (2011), 27-42. DOI 10.2140/involve.2011.4.27
  
• B. M. Ábrego, S. Fernández-Merchant, and B. Llano. An Inequality for Macaulay Functions. Journal of Integer Sequences 14 (2011), Article 11.7.4.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On crossing numbers of geometric proximity graphs. Computational Geometry 44 (2011), 216-233.
• B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, J. Leaños, and G. Salazar. There is a unique crossing-minimal rectilinear drawing of K18. Electronic Notes in Discrete Mathematics 38 (2011) 547-552.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, H. Meijer, V. Sacristán, M. Saumell. Proximity graphs inside large weighted graphs (extended abstract) , Proceedings of the 26th European Workshop on Computational Geometry (EuroCG'10), Dortmund, Germany, March 22-24 (2010) 9-12.
• B. M. Ábrego and S. Fernández-Merchant. Point-sets with many similar copies of a pattern: without a fixed number of collinear points or in parallelogram-free position. Geombinatorics 19 (2010), no. 4, 133-145.
• B. M. Ábrego and S. Fernández-Merchant. Point-sets in general position with many similar copies of a pattern. Geombinatorics 19 (2010), no. 3, 81-99.
• B. M. Ábrego, M. Cetina, S. Fernández-Merchant, J. Leaños, and G. Salazar. 3-symmetric and 3-decomposable drawings of Kn. Discrete Applied Mathematics 158 (2010), no. 12, 1240-1258.
• B. M. Ábrego, S. Fernández-Merchant, and B. Llano. On the maximum number of translates in a point set. Discrete and Computational Geometry, 43 (2010), 1-20.
• B. M. Ábrego, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On geometric proximity graphs. Proceedings of XIII Encuentros de Geometría Computacional, Universidad de Zaragoza, Spain, June 29-July 1, (2009) 151-156.
• B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with squares. Discrete and Computational Geometry 41 (2009), 77-95.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Sum of squares of degrees in a graph. Journal of Inequalities in Pure and Applied Mathematics, 10(3) (2009), Art. 64, 34 pp.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. A central approach to bound the number of crossings in a generalized configuration. Electronic Notes in Discrete Mathematics 30 (2008) 273-278.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. The maximum number of halving lines and the rectilinear crossing number of Kn for n<=27. Electronic Notes in Discrete Mathematics 30 (2008) 261-266.
• B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. An extended lower bound on the number of (<=k)-edges to generalized configurations of points and the pseudolinear crossing number of Kn. Journal of Combinatorial Theory, Series A. 115 (2008), 1257-1264.
• B. M. Ábrego, S. Fernández-Merchant, J. Leaños, and G. Salazar. Recent developments on the number of (<=k)-sets, halving-lines, and the rectilinear crossing number of Kn. Proceedings of XII Encuentros de Geometría Computacional, Universidad de Valladolid, Spain, June 25-27, (2007), ISBN 978-84-690-6900-4.
• B. M. Ábrego and S. Fernández-Merchant. Geometric drawings of Kn with few crossings. Journal of Combinatorial Theory, Series A 114 (2007) 373-379.
• B. M. Ábrego, J. Balogh, S. Fernández-Merchant, J. Leaños, and G. Salazar. On (<=k)–pseudoedges in generalized configurations and the pseudolinear crossing number of Kn. Preprint (2006).
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Trace-minimal graphs and D-optimal weighing designs, Linear Algebra and its Applications 412 (2006), 161-221.
• B. M. Ábrego and S. Fernández-Merchant. A lower bound for the rectilinear crossing number. Graphs and Combinatorics, Springer-Verlag Tokyo Inc., Vol. 21, Num 3, (2005), p. 293 - 300.
• B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with geometric objects: combinatorial results. Discrete and Computational Geometry Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004. Springer-Verlag, Lecture Notes in Computer Science Series, Vol. 3742, Akiyama, Jin; Kano, Mikio; Tan, Xuehou (Eds.) 2005, VIII, p. 1-15, ISBN: 3-540-30467-3.
• B. M. Ábrego, S. Fernández-Merchant, and Gy. Elekes. Structural results for planar sets with many similar subsets. Combinatorica 24 (2004), no. 4, 541-554.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. D-optimal weighing designs for n=-1 (mod 4) objects and a large number of weighings, Linear Algebra and its Applications 374 (2003), 175-218.
• B. M. Ábrego, S. Fernández-Merchant, M. G. Neubauer, and W. Watkins. Maximum volume simplices and trace-minimal graphs, Proceedings of X Encuentros de Geometria Computacional, University of Sevilla, Sevilla Spain, June 16-17, (2003), 51-56.
• B. M. Ábrego and S. Fernández-Merchant. The unit distance problem for centrally symmetric convex polygons. Discrete and computational geometry and graph drawing (Columbia, SC, 2001). Discrete and Computational Geometry 28 (2002), no 4, 467-473.
• B. M. Ábrego and S. Fernández-Merchant. Convex Polyhedra in R^3 Spanning W(n^(4/3)) Congruent Triangles, Journal of Combinatorial Theory, Series A 98, 406-409 (2002).
• B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles II. DIMACS Technical Report 99-47, (1999).
• B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles I. Discrete and Computational Geometry 23, (2000), no. 1, 129-115.
• B. M. Ábrego, J. L. Arocha, S. Fernández-Merchant, and V. Neumann-Lara. Tightness Problems in the Plane. Discrete Mathematics 194 (1999), no. 1-3, 1-11.
• B. M. Ábrego, Problemas Combinatorios Sobre Conjuntos Finitos de Puntos (Combinatorial Problems on Finite Sets). Aportaciones Matemáticas: Comunicaciones 19, SMM, Mexico (1997), ii+177pp, (1997) ISBN 968-36-5771-0.
• B. M. Ábrego, El Teorema de Sylvester (Sylvester's Theorem), Miscelánea Matemática, 23 (1996), 17-26.