"Swanepoel, Konrad"

Article

Volz, Marcus G., Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad and Thomas, Doreen A. (2012) The Gilbert arborescence problem. Networks, 61 (3). pp. 238-247. ISSN 0028-3045

Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad and Thomas, Doreen A. (2011) Generalised k-steiner tree problems in normed planes. Algorithmica . ISSN 1432-0541

Martini, Horst, Spirova, Margarita and Swanepoel, Konrad (2011) Geometry where direction matters—or does it? The mathematical intelligencer, 33 (3). pp. 115-125. ISSN 0343-6993

Pretorius, Lou M. and Swanepoel, Konrad (2011) Embedding a Latin square with transversal into a projective space. Journal of combinatorial theory, series A, 118 (5). pp. 1674-1683. ISSN 0097-3165

Swanepoel, Konrad (2011) Midpoint sets contained in the unit sphere of a normed space. Studia scientiarum mathematicarum hungarica, 48 (2). pp. 180-192. ISSN 0081-6906

Swanepoel, Konrad and Valtr, Pavel (2010) Large convexly independent subsets of Minkowski sums. Electronic journal of combinatorics , 17 (1). ISSN 1077-8926

Swanepoel, Konrad, Martini, Horst and Oloff de Wet, P. (2009) Absorbing angles, Steiner minimal trees and antipodality. Journal of optimization theory and applications, 143 (1). pp. 149-157. ISSN 0022-3239

Swanepoel, Konrad (2009) Simultaneous packing and covering in sequence spaces. Discrete and computational geometry, 42 (2). pp. 335-340. ISSN 0179-5376

Csikós, Balázs, Kiss, György, Swanepoel, Konrad and Oloff de Wet, P. (2009) Large antipodal families. Periodica mathematica Hungarica, 58 (2). pp. 129-138. ISSN 0031-5303

Pretorius, Lou M. and Swanepoel, Konrad (2009) The Sylvester-Gallai theorem, colourings and algebra. Discrete mathematics, 309 (2). pp. 385-399. ISSN 0012-365X

Swanepoel, Konrad (2009) Unit distances and diameters in Euclidean spaces. Discrete and computational geometry, 41 (1). pp. 1-27. ISSN 0179-5376

Swanepoel, Konrad (2009) Triangle-free minimum distance graphs in the plane. Geombinatorics quarterly, 19 (1). pp. 28-30. ISSN 1065-7371

Solymosi, József and Swanepoel, Konrad (2008) Elementary incidence theorems for complex numbers and quaternions. SIAM journal on discrete mathematics, 22 (3). pp. 1145-1148. ISSN 0895-4801

Swanepoel, Konrad and Villa, Rafael (2008) A lower bound for the equilateral number of normed spaces. Proceedings of the mathematical society, 136 (1). pp. 127-131. ISSN 0002-9939

Swanepoel, Konrad (2008) A new proof of Vázsonyi's conjecture. Journal of combinatorial theory, series A, 115 (5). pp. 888-892. ISSN 0097-3165

Swanepoel, Konrad (2007) Upper bounds for edge-antipodal and subequilateral polytopes. Periodica mathematica Hungarica, 54 (1). pp. 99-106. ISSN 0031-5303

Pretorius, Lou M. and Swanepoel, Konrad (2007) A generalised Sylvester-Gallai theorem. Die Suid-Afrikaanse tydskrif vir natuurwetenskap en tegnologie, 26 (1). pp. 8-13. ISSN 0254-3486

Swanepoel, Konrad (2007) The local Steiner problem in finite-dimensional normed spaces. Discrete and computational geometry, 37 (3). pp. 419-442. ISSN 0179-5376

Martini, Horst and Swanepoel, Konrad (2006) Antinorms and Radon curves. Aequationes mathematicae, 72 (1-2). pp. 110-138. ISSN 0001-9054

Pretorius, Lou M. and Swanepoel, Konrad (2006) Blockings sets in small finite linear spaces. Ars combinatoria, 80 . pp. 275-315. ISSN 0381-7032

Elkies, Noam, Pretorius, Lou M. and Swanepoel, Konrad (2006) Sylvester-Gallai theorems for complex numbers and quaternions. Discrete and computational geometry, 35 (3). pp. 361-373. ISSN 0179-5376

Martini, Horst and Swanepoel, Konrad (2006) Low-degree minimal spanning trees in normed spaces. Applied mathematics letters, 19 (2). pp. 122-125. ISSN 0893-9659

Swanepoel, Konrad and Schurmann, Achill (2006) Three-dimensional antipodal and norm-equilateral sets. Pacific journal of mathematics, 228 (2). pp. 349-370. ISSN 0030-8730

De Bonis, Annalisa, Katona, Gyula O. H. and Swanepoel, Konrad (2005) Largest family without A union B contained in C intersect D. Journal of combinatorial theory, series A, 111 (2). pp. 331-336. ISSN 0097-3165

Swanepoel, Konrad (2005) Quantitative illumination of convex bodies and vertex degrees of geometric Steiner minimal trees. Mathematika, 52 (1). pp. 47-52. ISSN 0025-5793

Swanepoel, Konrad (2004) A problem of Kusner on equilateral sets. Archiv der mathematik, 83 (2). pp. 164-170. ISSN 0003-889X

Martini, Horst and Swanepoel, Konrad (2004) Equiframed curves - a generalization of Radon curves. Monatshefte fur mathematik, 141 (4). pp. 301-314. ISSN 0026-9255

Pretorius, Lou M. and Swanepoel, Konrad (2004) An algorithmic proof of the Motzkin-Rabin theorem. American mathematical monthly, 111 (3). pp. 245-251. ISSN 0002-9890

Martini, Horst and Swanepoel, Konrad (2004) Non-planar simplices are not reduced. Publicationes mathematicae Debrecen, 64 (1-2). pp. 101-106. ISSN 0033-3883

Martini, Horst and Swanepoel, Konrad (2004) The geometry of Minkowski spaces - a survey. Part II. Expositiones mathematicae, 22 (2). pp. 93-144. ISSN 0723-0869

Martini, Horst and Swanepoel, Konrad (2003) Generalized convexity notions and combinatorial geometry. Congressus numerantium, 164 . pp. 65-93. ISSN 0384-9864

Swanepoel, Konrad (2003) Helly-type theorems for homothets of planar convex curves. Proceedings of the mathematical society, 131 (3). pp. 921-932. ISSN 0002-9939

Martini, Horst, Swanepoel, Konrad and Weiss, Gunter (2002) The Fermat-Torricelli problem in normed planes and spaces. Journal of optimization theory and applications, 115 (2). pp. 283-314. ISSN 0022-3239

Swanepoel, Konrad (2002) Independence numbers of planar contact graphs. Discrete and computational geometry, 28 (4). pp. 649-670. ISSN 0179-5376

Swanepoel, Konrad (2002) Helly-type theorems for polygonal curves. Discrete mathematics, 254 (1-3). pp. 527-537. ISSN 0012-365X

Brass, Peter, Rote, Gunter and Swanepoel, Konrad (2001) Triangles of extremal area or perimeter in a finite planar point set. Discrete and computational geometry, 26 (1). pp. 51-58. ISSN 0179-5376

Martini, Horst, Swanepoel, Konrad and Weiss, Gunter (2001) The geometry of Minkowski spaces - a survey. Part I. Expositiones mathematicae, 19 (2). pp. 97-142. ISSN 0723-0869

Swanepoel, Konrad (2000) Sets of unit vectors with small pairwise sums. Quaestiones mathematicae, 23 (3). pp. 383-288. ISSN 1607-3606

Swanepoel, Konrad (2000) The local Steiner problem in normed planes. Networks, 36 (2). pp. 104-113. ISSN 1097-0037

Swanepoel, Konrad (2000) Gaps in convex disc packings with an application to 1-Steiner minimum trees. Monatshefte fur mathematik, 129 (3). pp. 217-226. ISSN 0026-9255

Swanepoel, Konrad (2000) Balancing unit vectors. Journal of combinatorial theory, series A, 89 (1). pp. 105-112. ISSN 0097-3165

Swanepoel, Konrad (2000) On the existence of shortest directed networks. Journal of combinatorial mathematics and combinatorial computing, 33 . pp. 97-102. ISSN 0835-3026

Swanepoel, Konrad (1999) New lower bounds for the Hadwiger numbers of ℓp balls for p < 2. Applied mathematics letters, 12 (5). pp. 57-60. ISSN 0893-9659

Swanepoel, Konrad (1999) Vertex degrees of Steiner minimal trees in ℓ p d and other smooth Minkowski spaces. Discrete and computational geometry, 21 (3). pp. 437-447. ISSN 0179-5376

Swanepoel, Konrad (1999) Partitions of sets in metric and normed spaces induced by concentric spheres and parallel hyperplanes. Die Suid-Afrikaanse tydskrif vir natuurwetenskap en tegnologie, 18 . pp. 116-119. ISSN 0254-3486

Swanepoel, Konrad (1999) Cardinalities of k-distance sets in Minkowski spaces. Discrete mathematics, 197/19 . pp. 759-767. ISSN 0012-365X

Swanepoel, Konrad (1999) Helly-type theorems for hollow axis-aligned boxes. Proceedings of the mathematical society, 127 (7). pp. 2155-2162. ISSN 0002-9939

Swanepoel, Konrad (1996) Extremal problems in Minkowski space related to minimal networks. Proceedings of the mathematical society, 124 (8). pp. 2513-2518. ISSN 0002-9939

Book Section

Volz, M. G., Brazil, M., Swanepoel, Konrad and Thomas, D. A. (2009) Designing optimal flow networks. In: Ao, S. I., Gelman, L., Hukins, David W. L., Korsunsky, A. M. and Hunter, Andrew, (eds.) Proceedings of the World Congress on Engineering 2009. Newswood Ltd., London, UK, pp. 1235-1240. ISBN 9789881821010

Swanepoel, Konrad (2004) Equilateral sets in finite-dimensional normed spaces. In: Girela, Daniel, López Acedo, Gernaro and Villa Caro, Rafael, (eds.) Seminar of mathematical analysis. Secretariado de Publicationes, Universidad de Sevilla, Seville, Spain, pp. 195-237. ISBN 9788447208579

Swanepoel, Konrad and Valtr, P. (2004) The unit distance problem on spheres. In: Pach, János, (ed.) Towards a theory of geometric graphs. Contemporary mathematics (342). American mathematical society, Budapest, Hungary, pp. 273-280. ISBN 9780821834848

Monograph

Swanepoel, Konrad and Villa, Rafael (2011) Maximal equilateral sets. arXiv.

Conference or Workshop Item

Martini, Horst, Swanepoel, Konrad and Weiss, G. (2003) Some location problems in normed linear spaces. In: Dresden Symposium Geometrie: konstruktiv & kinematisch, 27 February - 1 March 2003, Dresden, Germany.