Classes
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Publications
- B. M. Ábrego and S. Fernández-Merchant, The
crossing number of centrally symmetric complete geometric
graphs, Electron. Notes Theor. Comput. Sci., (2021).
- B. M. Ábrego and S. Fernández-Merchant, A. Sparks, The bipartite-cylindrical crossing number of the complete bipartite graph, Graphs Combin. 36 (2020) 205–220. http://doi:10.1007/s00373- 019-02076-5.
- B. M. Ábrego and S. Fernández-Merchant, E. Lagoda, P. Ramos, On the crossing number of 2-page book drawings of Kn with prescribed number of edges in each page, Graphs and Combinatorics 36 (2020) 303–318 https://doi.org/10.1007_/s00373-019-02077-4.
- B.
M.
Ábrego, S. Fernández-Merchant, M. Kano, D.
Orden, P. Pérez-Lantero, C. Seara, and J.
Tejel, K1,3-covering red and
blue points in the plane, Disc. Math.
& Theor. Comp. Sci. 21-3
(2019) Paper No. 6, 29 pp.
- C.
Camacho, S. Fernández-Merchant, M. Jelić
Milutinović, R. Kirsch, L. Kleist, E.
Matson, and J. White, Bounding
the tripartite circle crossing number of
complete tripartite graphs. Acta Math.
Univ. Comenian 88-3 (2019) 515–520.
- B. M. Ábrego and S. Fernández-Merchant, On the convex crossing number. In Proc. JCDCG3, Tokyo University of Science, Tokyo, Japan (2019).
- B.
M. Ábrego, S. Fernández-Merchant, A. P.
Figueroa, J. J. Montellano-Ballesteros, and
E. Rivera-Campo, Crossings in
twisted graphs. In Proc. JCDCG3, Tokyo
University of Science, Tokyo, Japan (2019).
- B. M. Ábrego, O. Aichholzer, S. Fernández-Merchant, D. McQuillan, B. Mohar, P. Mutzel, P. Ramos, R. B. Richter, and B. Vogtenhuber, Bishellable drawings of Kn, SIAM J. Discrete Math. 32-4 (2018) 2482–2492.
- C.
Camacho, S. Fernández-Merchant, M. Jelic, R.
Kirsch, L. Kleist, E. Bailey Matson, and J
White, Bounding
the tripartite circle crossing number of
complete tripartite graphs. 26th
International Symp. on Graph Drawing and
Network Visualization, U. Politècnica de
Catalunya, Barcelona, Spain (2018).
- B.
M. Ábrego, K. Dondzila, S.
Fernández-Merchant, L. Evgeniya, S. Seyed,
and S. Yakov, On
the rectilinear local crossing number of Km,n, J. Inform.
Process. 25 (2017) 1–9.
- B. M. Ábrego and S. Fernández-Merchant, The rectilinear local crossing number of Kn, J. Combin. Theory Ser. A 151 (2017) 131–145. (arXiv:1508.07926)
- B. M.
Ábrego, S.
Fernández-Merchant, and A.
Sparks. The
bipartite cylindrical
crossing number of Km,n.
In Proc. JCDCG3, Tokyo
University of Science,
Tokyo, Japan (2017).
- B. M.
Ábrego, S.
Fernández-Merchant, E.
Lagoda, and P. Ramos.
Minimizing crossings of
2-page drawings of Kn with
prescribed number of edges
in each page. In Proc.
JCDCG3, Tokyo University of
Science, Tokyo, Japan
(2017).
- B. M.
Ábrego, O. Aichholzer, S.
Fernández-Merchant, D.
McQuillan, B. Mohar, P.
Mutzel, P. Ramos, R. B.
Richter, and B. Vogtenhuber.
Bishellable drawings of Kn.
In Proc. 17th Spanish
Meeting on Comp. Geom.,
Alicante, Spain (2017).
- B. M.
Ábrego, J. Dandurand , S.
Fernández-Merchant, L.
Evgeniya, and S. Yakov,
Further improvements on the
book crossing number of Kn.
In Proc. 17th Spanish
Meeting on Comp. Geom.,
Alicante, Spain (2017).
- B. M. Ábrego, S. Fernández-Merchant, M. Kano, D. Orden, P. Pérez-Lantero, C. Seara, and J. Tejel. Star covering of red and blue points in the plane. In Proc. 33rd European Workshop on Comp. Geom. (EuroCG), Malmö, Sweden, (2017). (arXiv:1707.06856)
- B. M. Ábrego, S. Fernández-Merchant, D. J. Katz, and L. Kolesnikov. On the number of similar instances of a pattern in a finite set, Electron. J. Combin. 23-4 (2016) #P4.39. (arXiv:1501.00076)
- B.
M.
Ábrego, J. Dandurand, S. Fernández-Merchant,
E. Lagoda, and Y. Sapozhnikov, Book crossing
numbers of the complete graph and small
convex local crossing numbers (2016) arXiv:1607.00131.
- B. M. Ábrego, J. Dandurand, S. Fernández-Merchant, E. Lagoda, and Y. Sapozhnikov. Improved lower bounds on book crossing numbers of Kn. Proceedings JCDCG3, Tokyo University of Science (2016).
- B. M. Ábrego, S. Fernández-Merchant, E. Lagoda, Y. Sapozhnikov, A. Olavarrieta, K. Dondzila and S. Sajjadi. The rectilinear local crossing number of Kn,m. Proceedings JCDCG3, Tokyo University of Science (2016).
- B. M. Ábrego, S. Fernández-Merchant, and D. Flores-Peñaloza. New bounds on the maximum number of locally non-overlapping triangles in the plane, Proceedings JCDCG3, Tokyo University of Science (2016).
- 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
(2013) 411–414.
- 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, S. Fernández-Merchant, and G. Salazar. The rectilinear crossing number of Kn: Closing in (or are we?). In Thirty essays in geometric graph theory, J. Pach (Ed), Springer (2013), XVI, 504 p.
- 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 B. Llano. An inequality for Kruskal-Macaulay Functions, Journal of Integer Sequences, 14 (2011) Article 11.7.4.
- 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, 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), no. 1, 192-215.
- 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, S. Fernández-Merchant, D. B. Roberts. On the maximum number of isosceles right triangles in a finite point set. Involve 4 (2011), no. 1, 27–42.
- 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, R. Fábila, S. Fernández-Merchant, D. Flores, F. Hurtado, V. Sacristán, M. Saumell. On crossings in 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 (2009), no. 3, Art. 64, 34 pp.
- 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, 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., 21 (2005), no. 3, 293 - 300.
- B. M. Ábrego, E. Arkin, S. Fernández-Merchant, F. Hurtado, M. Kano, J. Mitchell, J. Urrutia. Matching points with circles and squares. Discrete and computational geometry, 1-15, Lecture Notes in Comput. Sci., 3742, Springer, Berlin, 2005. 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 (2002), 406-409.
- B. M. Ábrego and S. Fernández-Merchant. On the Maximum Number of Equilateral Triangles II. DIMACS Technical Report (1999), 99-47.
- 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.