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Lavollée, Jérémy and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2023)
A tight bound for the number of edges of matchstick graphs.
Discrete and Computational Geometry.
ISSN 0179-5376
Lavollée, Jérémy and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2023)
The number of small-degree vertices in matchstick graphs.
Australasian Journal of Combinatorics, 85 (1).
92 - 99.
ISSN 2202-3518
Lavollée, Jérémy and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2022)
Bounding the number of edges of matchstick graphs.
SIAM Journal on Discrete Mathematics, 36 (1).
777 - 785.
ISSN 0895-4801
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2021)
Outer linear measure of connected sets via Steiner trees.
Real Analysis Exchange, 46 (1).
207 - 232.
ISSN 0147-1937
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2021)
Triangles of nearly equal area.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 62 (1).
219 - 227.
ISSN 0138-4821
Lin, Aaron and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2021)
Ordinary hyperspheres and spherical curves.
Advances in Geometry, 21 (1).
15 - 22.
ISSN 1615-715X
Naszódi, Márton, Prokaj, Vilmos and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2020)
Angular measures and Birkhoff orthogonality in Minkowski planes.
Aequationes Mathematicae, 94 (5).
969 - 977.
ISSN 0001-9054
Maxwell, Alastair and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2020)
Shortest directed networks in the plane.
Graphs and Combinatorics, 36 (5).
1457 - 1475.
ISSN 0911-0119
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2020)
Favourite distances in 3-space.
Electronic Journal of Combinatorics, 27 (2).
pp. 1-11.
ISSN 1077-8926
Balko, Martin, Por, Attila, Scheucher, Manfred, Swanepoel, Konrad ORCID: 0000-0002-1668-887X and Valtr, Pavel
(2020)
Almost-equidistant sets.
Graphs and Combinatorics, 36 (3).
729 - 754.
ISSN 0911-0119
Lin, Aaron and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2020)
On sets defining few ordinary hyperplanes.
Discrete Analysis.
ISSN 2397-3129
Frankl, Nóra, Kupavskii, Andrey and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2020)
Embedding graphs in Euclidean space.
Journal of Combinatorial Theory, Series A, 171.
ISSN 0097-3165
Lin, A and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2019)
Ordinary planes, coplanar quadruples, and space quartics.
Journal of the London Mathematical Society, 100 (3).
pp. 937-956.
ISSN 0024-6107
Kupavskii, Andrey, Mustafa, Nabil H. and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2019)
Bounding the size of an almost-equidistant set in Euclidean space.
Combinatorics, Probability and Computing, 28 (2).
pp. 280-286.
ISSN 0963-5483
Naszódi, Márton and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2018)
Arrangements of homothets of a convex body II.
Contributions to Discrete Mathematics, 13 (2).
116 - 123.
ISSN 1715-0868
Lin, Aaron, Makhul, Mehdi, Mojarrad, Hossein Nassajian, Schicho, Josef, Swanepoel, Konrad ORCID: 0000-0002-1668-887X and de Zeeuw, Frank
(2018)
On sets defining few ordinary circles.
Discrete and Computational Geometry, 59 (1).
pp. 59-87.
ISSN 0179-5376
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2018)
Combinatorial distance geometry in normed spaces.
In: Ambrus, Gergely, Barany, Imre, Boroczky, Karoly J., Fejes Toth, Gabor and Pach, János, (eds.)
New Trends in Intuitive Geometry.
Bolyai Society Mathematical Studies.
Springer Berlin / Heidelberg, Berlin, Germany, 407 - 458.
ISBN 9783662574126
Naszódi, Márton, Pach, János and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2018)
Sphere-of-influence graphs in normed spaces.
In:
Discrete Geometry and Symmetry: In Honor of Károly Bezdek’s and Egon Schulte’s 60th Birthdays.
Springer International (Firm), Cham, Switzerland.
Naszódi, Márton, Pach, János and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2017)
Arrangements of homothets of a convex body.
Mathematika, 63 (2).
696 - 710.
ISSN 0025-5793
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2016)
Sets of unit vectors with small subset sums.
Transactions of the American Mathematical Society, 368 (10).
7153 - 7188.
ISSN 0002-9947
Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad ORCID: 0000-0002-1668-887X and Thomas, Doreen A.
(2015)
Generalised k-Steiner tree problems in normed planes.
Algorithmica, 71 (1).
pp. 66-86.
ISSN 1432-0541
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2014)
Book review: Beautiful geometry by Eli Maor and Eugen Jost.
LSE Review of Books
(03 Mar 2014).
Website.
Volz, Marcus G., Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad ORCID: 0000-0002-1668-887X and Thomas, Doreen A.
(2012)
The Gilbert arborescence problem.
Networks, 61 (3).
pp. 238-247.
ISSN 0028-3045
Martini, Horst, Spirova, Margarita and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2011)
Geometry where direction matters—or does it?
Mathematical Intelligencer, 33 (3).
pp. 115-125.
ISSN 0343-6993
Pretorius, Lou M. and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X and Valtr, Pavel
(2010)
Large convexly independent subsets of Minkowski sums.
Electronic Journal of Combinatorics, 17 (1).
ISSN 1077-8926
Swanepoel, Konrad ORCID: 0000-0002-1668-887X, 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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X 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 ORCID: 0000-0002-1668-887X
(2009)
The Sylvester-Gallai theorem, colourings and algebra.
Discrete Mathematics, 309 (2).
pp. 385-399.
ISSN 0012-365X
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2009)
Unit distances and diameters in Euclidean spaces.
Discrete and Computational Geometry, 41 (1).
pp. 1-27.
ISSN 0179-5376
Volz, M. G., Brazil, M., Swanepoel, Konrad ORCID: 0000-0002-1668-887X 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 ORCID: 0000-0002-1668-887X
(2009)
Triangle-free minimum distance graphs in the plane.
Geombinatorics Quarterly, 19 (1).
pp. 28-30.
ISSN 1065-7371
Solymosi, József and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2008)
Elementary incidence theorems for complex numbers and quaternions.
SIAM Journal on Discrete Mathematics, 22 (3).
pp. 1145-1148.
ISSN 0895-4801
Swanepoel, Konrad ORCID: 0000-0002-1668-887X 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 ORCID: 0000-0002-1668-887X
(2008)
A new proof of Vázsonyi's conjecture.
Journal of Combinatorial Theory, Series A, 115 (5).
pp. 888-892.
ISSN 0097-3165
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(2007)
A generalised Sylvester-Gallai theorem.
Die Suid-Afrikaanse Tydskrif Vir Natuurwetenskap En Tegnologie, 26 (1).
pp. 8-13.
ISSN 0254-3486
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(2006)
Antinorms and Radon curves.
Aequationes Mathematicae, 72 (1-2).
pp. 110-138.
ISSN 0001-9054
Pretorius, Lou M. and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(2006)
Low-degree minimal spanning trees in normed spaces.
Applied Mathematics Letters, 19 (2).
pp. 122-125.
ISSN 0893-9659
Swanepoel, Konrad ORCID: 0000-0002-1668-887X 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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(2004)
A problem of Kusner on equilateral sets.
Archiv Der Mathematik, 83 (2).
pp. 164-170.
ISSN 0003-889X
Martini, Horst and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(2004)
An algorithmic proof of the Motzkin-Rabin theorem.
American Mathematical Monthly, 111 (3).
pp. 245-251.
ISSN 0002-9890
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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
Martini, Horst and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2004)
Non-planar simplices are not reduced.
Publicationes Mathematicae Debrecen, 64 (1-2).
pp. 101-106.
ISSN 0033-3883
Martini, Horst and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2004)
The geometry of Minkowski spaces - a survey. Part II.
Expositiones Mathematicae, 22 (2).
pp. 93-144.
ISSN 0723-0869
Swanepoel, Konrad ORCID: 0000-0002-1668-887X 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
Martini, Horst and Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2003)
Generalized convexity notions and combinatorial geometry.
Congressus Numerantium, 164.
pp. 65-93.
ISSN 0384-9864
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X and Weiss, G.
(2003)
Some location problems in normed linear spaces.
In: Dresden Symposium Geometrie: konstruktiv & kinematisch, 2003-02-27 - 2003-03-01, Dresden, Germany, DEU.
Martini, Horst, Swanepoel, Konrad ORCID: 0000-0002-1668-887X 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 ORCID: 0000-0002-1668-887X
(2002)
Independence numbers of planar contact graphs.
Discrete and Computational Geometry, 28 (4).
pp. 649-670.
ISSN 0179-5376
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X 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 ORCID: 0000-0002-1668-887X
(2000)
Sets of unit vectors with small pairwise sums.
Quaestiones Mathematicae, 23 (3).
pp. 383-288.
ISSN 1607-3606
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2000)
The local Steiner problem in normed planes.
Networks, 36 (2).
pp. 104-113.
ISSN 1097-0037
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(2000)
Balancing unit vectors.
Journal of Combinatorial Theory, Series A, 89 (1).
pp. 105-112.
ISSN 0097-3165
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(2000)
On the existence of shortest directed networks.
Journal of Combinatorial Mathematics and Combinatorial Computing, 33.
pp. 97-102.
ISSN 0835-3026
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(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 ORCID: 0000-0002-1668-887X
(1999)
Cardinalities of k-distance sets in Minkowski spaces.
Discrete Mathematics, 197/19.
pp. 759-767.
ISSN 0012-365X
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(1999)
Helly-type theorems for hollow axis-aligned boxes.
Proceedings of the Mathematical Society, 127 (7).
pp. 2155-2162.
ISSN 0002-9939
Swanepoel, Konrad ORCID: 0000-0002-1668-887X
(1996)
Extremal problems in Minkowski space related to minimal networks.
Proceedings of the Mathematical Society, 124 (8).
pp. 2513-2518.
ISSN 0002-9939