Swanepoel, Konrad

Dr Konrad Swanepoel  

Department

Position held

Associate Professor (Reader)

 

Experience keywords:

combinatorial and discrete geometry; convex geometry; geometric networks; geometry of finite-dimensional normed spaces

Languages:

Afrikaans [Spoken: Fluent, Written: Fluent]; German [Spoken: Intermediate, Written: Intermediate]

Contact Points

LSE phone number:

+44 (0)207 107 5095

Alt phone number:

+44 (0)207 955 7732/7925

Publications

2017

Swanepoel, Konrad (2017) Combinatorial distance geometry in normed spaces In: Ambrus, Gergely and Barany, Imre and Boroczky, Karoly J. and Fejes Toth, Gabor and Pach, János, (eds.) New Trends in Intuitive Geometry. Bolyai Society Mathematical Studies. Springer-Verlag, Berlin, Germany.

Naszódi, Márton and Pach, János and Swanepoel, Konrad (2017) Arrangements of homothets of a convex body Mathematika, 163 (2). 696-710. ISSN 0025-5793 (In Press)

Ras, Charl J. and Swanepoel, Konrad J. and Thomas, Doreen (2017) Approximate Euclidean Steiner trees Journal of Optimization Theory and Applications, 172 (3). 845-873. ISSN 0022-3239

Lin, Aaron and Makhul, Mehdi and Mojarrad, Hossein Nassajian and Schicho, Josef and Swanepoel, Konrad and de Zeeuw, Frank (2017) On sets defining few ordinary circles Discrete and Computational Geometry. 1-29. ISSN 0179-5376

2016

Swanepoel, Konrad (2016) Sets of unit vectors with small subset sums Transactions of the American Mathematical Society, 368 (10). 7153-7188. ISSN 0002-9947

2015

Brazil, Marcus and Ras, Charl J. and Swanepoel, Konrad and Thomas, Doreen A. (2015) Generalised k-Steiner tree problems in normed planes Algorithmica, 71 (1). 66-86. ISSN 1432-0541

Pach, János and Swanepoel, Konrad J. (2015) Double-normal pairs in the plane and on the sphere Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 56 (2). 423-438. ISSN 0138-4821

Pach, János and Swanepoel, Konrad J. (2015) Double-normal pairs in space Mathematika, 61 (1). 259-272. ISSN 0025-5793

2014

Swanepoel, Konrad (2014) Book review: Beautiful geometry by Eli Maor and Eugen Jost LSE Review of Books (3 Mar 2014) Blog entry

Swanepoel, Konrad J. (2014) Equilateral sets and a Schütte theorem for the 4-norm Canadian Mathematical Bulletin, 57 (3). 640-647. ISSN 0008-4395

2013

Swanepoel, Konrad J. and Villa, Rafael (2013) Maximal equilateral sets Discrete and Computational Geometry, 50 (2). 354-373. ISSN 0179-5376

2012

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

2011

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

Swanepoel, Konrad (2011) Midpoint sets contained in the unit sphere of a normed space Studia Scientiarum Mathematicarum Hungarica, 48 (2). 180-192. ISSN 0081-6906

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). 1674-1683. ISSN 0097-3165

2010

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

2009

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

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

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

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

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

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

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

2008

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

Swanepoel, Konrad (2008) A new proof of Vázsonyi's conjecture Journal of Combinatorial Theory, Series A, 115 (5). 888-892. ISSN 0097-3165

Solymosi, József and Swanepoel, Konrad (2008) Elementary incidence theorems for complex numbers and quaternions SIAM Journal on Discrete Mathematics, 22 (3). 1145-1148. ISSN 0895-4801

2007

Pretorius, Lou M. and Swanepoel, Konrad (2007) A generalised Sylvester-Gallai theorem Die Suid-Afrikaanse Tydskrif Vir Natuurwetenskap En Tegnologie, 26 (1). 8-13. ISSN 0254-3486

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

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

2006

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

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

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

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

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

2005

De Bonis, Annalisa and 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). 331-336. ISSN 0097-3165

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

2004

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

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

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, 273-280. ISBN 9780821834848

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

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

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

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

2003

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

Martini, Horst and 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

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

2002

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

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

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

2001

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

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

2000

Swanepoel, Konrad (2000) On the existence of shortest directed networks Journal of Combinatorial Mathematics and Combinatorial Computing, 33. 97-102. ISSN 0835-3026

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

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

Swanepoel, Konrad (2000) Balancing unit vectors Journal of Combinatorial Theory, Series A, 89 (1). 105-112. ISSN 0097-3165

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

1999

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

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. 116-119. ISSN 0254-3486

Swanepoel, Konrad (1999) New lower bounds for the Hadwiger numbers of ℓp balls for p Applied Mathematics Letters, 12 (5). 57-60. ISSN 0893-9659

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

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

1996

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

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