Publication list

Click here for a list of all my papers at arxiv.org, or click on a title to download a single paper. If a title is not clickable, send me an e-mail.

Exposition and survey

• Triangle-free minimum distance graphs in the plane. Geombinatorics 19 (2009), 28-30.
• Antinorms and Radon curves. With H. Martini. Aequationes Mathematicae 72 (2006), 110-138.
• Equilateral sets in finite-dimensional normed spaces. In: Seminar of Mathematical Analysis, eds. Daniel Girela Álvarez, Genaro López Acedo, Rafael Villa Caro, Secretariado de Publicationes, Universidad de Sevilla, Seville, 2004, pp. 195-237.
• The Geometry of Minkowski Spaces — a survey. Part II. With H. Martini. Expositiones Mathematicae 22 (2004), 93-144.
• Some location problems in normed linear spaces. With H. Martini and G. Weiss. Dresden Symposium Geometrie: konstruktiv & kinematisch, February 27—March 1, 2003, Dresden, Germany.
• Generalized Convexity Notions and Combinatorial Geometry. With H. Martini. Congressus Numerantium 164 (2003), 65-93.
• The geometry of Minkowski spaces — a survey. Part I. With H. Martini and G. Weiss. Expositiones Mathematicae 19 (2001) 97-142.

Research papers

• Embedding a Latin square with transversal into a projective space. With L. M. Pretorius. Submitted.
• Generalised k-Steiner Tree Problems in Normed Planes. With M. Brazil, C. Ras, and D. A. Thomas, submitted.
• Large convexly independent subsets of Minkowski sums. With P. Valtr, submitted.
  
• The Gilbert arborescence problem. With M. G. Volz, M. Brazil, C. Ras, and D. A. Thomas, submitted.
• Midpoint sets contained in the unit sphere of a normed space. accepted by Studia Sci. Math. Hungarica.
  
• Designing optimal flow networks. With M. G. Volz, M. Brazil, and D. A. Thomas, Proceedings of the World Congress on Engineering 2009 Vol II, WCE 2009, July 1 – 3, 2009, London, U.K. pp. 1235-1240.
• Absorbing angles, Steiner minimal trees and antipodality. With H. Martini and P. O. de Wet. Journal of Optimization Theory and Applications, 143 (2009), 149-157.
• Simultaneous packing and covering in sequence spaces. Discrete & Computational Geometry 42 (2009), 335–340.
• Large antipodal families. With B. Csikós, G. Kiss, and P. O. de Wet. Periodica Mathematica Hungarica 58 (2009), 129–138
• Unit distances and diameters in Euclidean spaces. Discrete & Computational Geometry 41 (2009), 1–27.
• The Sylvester-Gallai theorem, colourings and algebra. With L.M. Pretorius. Discrete Mathematics 309 (2009), 385–399.
• A new proof of Vázsonyi’s conjecture. Journal of Combinatorial Theory, Ser. A 115 (2008) 888–892.
• Elementary incidence theorems for complex numbers and quaternions. With József Solymosi. SIAM Journal on Discrete Mathematics 22 (2008), 1145-1148.
• A lower bound for the equilateral number of normed spaces. With Rafael Villa. Proceedings of the American Mathematical Society 136 (2008), 127-131.
• The local Steiner problem in finite-dimensional normed spaces. Discrete & Computational Geometry 37 (2007), 419–442.
• A generalised Sylvester-Gallai theorem. With Lou M. Pretorius. Die Suid-Afrikaanse Tydskrif vir Wetenskap en Tegnologie 26 (2007), 8–13. (Afrikaans. English Summary).
• Upper bounds for edge-antipodal and subequilateral polytopes. Periodica Mathematica Hungarica 54 (2007), 99–106.
• Three-dimensional antipodal and norm-equilateral sets. With Achill Schürmann. Pacific Journal of Mathematics 228 (2006), 349-370.
• Blocking sets in small finite linear spaces. With L.M. Pretorius. Ars Combinatoria 80 (2006) 275-315.
• Sylvester-Gallai Theorems for Complex Numbers and Quaternions. With Noam Elkies and Lou M. Pretorius. Discrete & Computational Geometry 35 (2006), 361-373.
• Low-degree minimal spanning trees in normed spaces. Applied Mathematics Letters 19 (2006), 122-125.
  With H. Martini.
• Quantitative illumination of convex bodies and vertex degrees of geometric Steiner minimal trees. Mathematika 52 (2005), 47-52.
• Largest family without A union B contained in C intersect D. With A. De Bonis and G.O.H. Katona. Journal of Combinatorial Theory, Ser. A. 111 (2005), 331-336.
• A problem of Kusner on equilateral sets . Archiv der Mathematik (Basel) 83 (2004), 164-170.
• Equiframed curves — a generalization of Radon curves. With H. Martini. Monatshefte für Mathematik 141 (2004), 301-314.
• Non-planar simplices are not reduced. With H. Martini. Publicationes Mathematicae Debrecen 64 (2004), 101-106.
• The unit distance problem on spheres. With P. Valtr. In: Towards a Theory of Geometric Graphs, Contemporary Mathematics 342, ed. János Pach, American Mathematical Society, 2004.
• An algorithmic proof of the Motzkin-Rabin theorem. With L.M. Pretorius. American Mathematical Monthly 111 no. 3 (2004), 245-251.
• Helly-type theorems for homothets of planar convex curves. Proceedings of the American Mathematical Society 131 (2003) 921-932.
• Independence numbers of planar contact graphs. Discrete & Computational Geometry 28 (2002) 649-670.
• The Fermat-Torricelli problem in normed planes and spaces. With H. Martini and G. Weiss. Journal of Optimization Theory and Applications 115 (2002) 283-314.
• Helly-type theorems for polygonal curves. Discrete Mathematics 254 (2002) 527-537.
• Triangles of extremal area or perimeter in a finite planar point set. With Peter Brass and Günter Rote. Discrete & Computational Geometry 26 (2001) 51-58.
• Sets of unit vectors with small pairwise sums. Quaestiones Mathematicae 23 (2000) 383-388.
• The local Steiner problem in normed planes. Networks 36 (2000) 104-113.
• On the existence of shortest directed networks. Journal of Combinatorial Mathematics and Combinatorial Computing 33 (2000) 97-102.
• Gaps in Convex Disc Packings with an Application to 1-Steiner Minimum Trees. Monatshefte für Mathematik 129 (2000) 217-226.
• Balancing unit vectors. Journal of Combinatorial Theory, Series A 89 (2000) 105-112.
• Partitions of sets in metric and normed spaces induced by concentric spheres and parallel hyperplanes. Suid-Afrikaanse Tydskrif vir Wetenskap en Tegnologie 18 (1999) 116-119 (Afrikaans. English Summary).
• Helly-type Theorems for Hollow Axis-aligned Boxes. Proceedings of the American Mathematical Society 127 (1999) 2155-2162.
• New lower bounds for the Hadwiger numbers of l_p balls for p<2. Applied Mathematics Letters 12 (1999) 57-60.
• Cardinalities of k-distance sets in Minkowski spaces. Discrete Mathematics 197/198 (1999) 759-767.
• Vertex degrees of Steiner Minimal Trees in l_p^d and other smooth Minkowski spaces. Discrete & Computational Geometry 21 (1999) 437-447.
• Extremal Problems in Minkowski Space related to Minimal Networks. Proceedings of the American Mathematical Society 124 (1996) 2513-2518.