Swanepoel, Konrad

Number of items: 83.
None
  • Pach, János, Swanepoel, Konrad J. (2015). Double-normal pairs in space. Mathematika, 61(1), 259-272. https://doi.org/10.1112/S0025579314000217
  • Brazil, M., Ras, C.J., Swanepoel, Konrad J., Thomas, D. A. (2014). The centroid as an estimate for the quadratic min-power centre. In Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (pp. 800-803). University of Groningen.
  • Volz, Marcus G., Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad, Thomas, Doreen A. (2012). The Gilbert arborescence problem. Networks, 61(3), 238-247. https://doi.org/10.1002/net.21475
  • Martini, Horst, Spirova, Margarita, Swanepoel, Konrad (2011). Geometry where direction matters—or does it? Mathematical Intelligencer, 33(3), 115-125. https://doi.org/10.1007/s00283-011-9233-4
  • Pretorius, Lou M., Swanepoel, Konrad (2011). Embedding a Latin square with transversal into a projective space. Journal of Combinatorial Theory, Series A, 118(5), 1674-1683. https://doi.org/10.1016/j.jcta.2011.01.013
  • Swanepoel, Konrad (2011). Midpoint sets contained in the unit sphere of a normed space. Studia Scientiarum Mathematicarum Hungarica, 48(2), 180-192. https://doi.org/10.1556/SScMath.48.2011.2.1165
  • Swanepoel, Konrad, Valtr, Pavel (2010). Large convexly independent subsets of Minkowski sums. Electronic Journal of Combinatorics, 17(1).
  • Swanepoel, Konrad, Martini, Horst, Oloff de Wet, P. (2009). Absorbing angles, Steiner minimal trees and antipodality. Journal of Optimization Theory and Applications, 143(1), 149-157. https://doi.org/10.1007/s10957-009-9552-1
  • Swanepoel, Konrad (2009). Simultaneous packing and covering in sequence spaces. Discrete and Computational Geometry, 42(2), 335-340. https://doi.org/10.1007/s00454-009-9189-8
  • Csikós, Balázs, Kiss, György, Swanepoel, Konrad, Oloff de Wet, P. (2009). Large antipodal families. Periodica Mathematica Hungarica, 58(2), 129-138. https://doi.org/10.1007/s10998-009-10129-9
  • Pretorius, Lou M., Swanepoel, Konrad (2009). The Sylvester-Gallai theorem, colourings and algebra. Discrete Mathematics, 309(2), 385-399. https://doi.org/10.1016/j.disc.2007.12.027
  • Swanepoel, Konrad (2009). Unit distances and diameters in Euclidean spaces. Discrete and Computational Geometry, 41(1), 1-27. https://doi.org/10.1007/s00454-008-9082-x
  • Volz, M. G., Brazil, M., Swanepoel, Konrad, Thomas, D. A. (2009). Designing optimal flow networks. In Ao, S. I., Gelman, L., Hukins, D. W. L., Korsunsky, A. M. & Hunter, A. (Eds.), Proceedings of the World Congress on Engineering 2009 (pp. 1235-1240). Newswood Ltd..
  • Swanepoel, Konrad (2009). Triangle-free minimum distance graphs in the plane. Geombinatorics Quarterly, 19(1), 28-30.
  • Solymosi, József, Swanepoel, Konrad (2008). Elementary incidence theorems for complex numbers and quaternions. SIAM Journal on Discrete Mathematics, 22(3), 1145-1148. https://doi.org/10.1137/070685117
  • Swanepoel, Konrad, Villa, Rafael (2008). A lower bound for the equilateral number of normed spaces. Proceedings of the Mathematical Society, 136(1), 127-131. https://doi.org/10.1090/S0002-9939-07-08916-2
  • Swanepoel, Konrad (2008). A new proof of Vázsonyi's conjecture. Journal of Combinatorial Theory, Series A, 115(5), 888-892. https://doi.org/10.1016/j.jcta.2007.08.006
  • Swanepoel, Konrad (2007). Upper bounds for edge-antipodal and subequilateral polytopes. Periodica Mathematica Hungarica, 54(1), 99-106. https://doi.org/10.1007/s-10998-007-1099-0
  • Pretorius, Lou M., Swanepoel, Konrad (2007). A generalised Sylvester-Gallai theorem. Die Suid-Afrikaanse Tydskrif Vir Natuurwetenskap En Tegnologie, 26(1), 8-13.
  • Swanepoel, Konrad (2007). The local Steiner problem in finite-dimensional normed spaces. Discrete and Computational Geometry, 37(3), 419-442. https://doi.org/10.1007/s00454-006-1298-z
  • Martini, Horst, Swanepoel, Konrad (2006). Antinorms and Radon curves. Aequationes Mathematicae, 72(1-2), 110-138. https://doi.org/10.1007/s00010-006-2825-y
  • Pretorius, Lou M., Swanepoel, Konrad (2006). Blockings sets in small finite linear spaces. Ars Combinatoria, 80, 275-315.
  • Elkies, Noam, Pretorius, Lou M., Swanepoel, Konrad (2006). Sylvester-Gallai theorems for complex numbers and quaternions. Discrete and Computational Geometry, 35(3), 361-373. https://doi.org/10.1007/s00454-005-1226-7
  • Martini, Horst, Swanepoel, Konrad (2006). Low-degree minimal spanning trees in normed spaces. Applied Mathematics Letters, 19(2), 122-125. https://doi.org/10.1016/j.aml.2005.03.011
  • Swanepoel, Konrad, Schurmann, Achill (2006). Three-dimensional antipodal and norm-equilateral sets. Pacific Journal of Mathematics, 228(2), 349-370.
  • De Bonis, Annalisa, Katona, Gyula O. H., Swanepoel, Konrad (2005). Largest family without A union B contained in C intersect D. Journal of Combinatorial Theory, Series A, 111(2), 331-336. https://doi.org/10.1016/j.jcta.2005.01.002
  • Swanepoel, Konrad (2005). Quantitative illumination of convex bodies and vertex degrees of geometric Steiner minimal trees. Mathematika, 52(1), 47-52. https://doi.org/10.1112/S0025579300000322
  • Swanepoel, Konrad (2004). A problem of Kusner on equilateral sets. Archiv Der Mathematik, 83(2), 164-170. https://doi.org/10.1007/s00013-003-4840-8
  • Martini, Horst, Swanepoel, Konrad (2004). Equiframed curves - a generalization of Radon curves. Monatshefte fur Mathematik, 141(4), 301-314. https://doi.org/10.1007/s00605-003-0052-3
  • Pretorius, Lou M., Swanepoel, Konrad (2004). An algorithmic proof of the Motzkin-Rabin theorem. American Mathematical Monthly, 111(3), 245-251.
  • Swanepoel, Konrad (2004). Equilateral sets in finite-dimensional normed spaces. In Girela, D., López Acedo, G. & Villa Caro, R. (Eds.), Seminar of Mathematical Analysis (pp. 195-237). Universidad de Sevilla. Secretariado de Publicaciones.
  • Martini, Horst, Swanepoel, Konrad (2004). Non-planar simplices are not reduced. Publicationes Mathematicae Debrecen, 64(1-2), 101-106.
  • Martini, Horst, Swanepoel, Konrad (2004). The geometry of Minkowski spaces - a survey. Part II. Expositiones Mathematicae, 22(2), 93-144. https://doi.org/10.1016/S0723-0869(04)80009-4
  • Swanepoel, Konrad, Valtr, P. (2004). The unit distance problem on spheres. In Pach, J. (Ed.), Towards a Theory of Geometric Graphs (pp. 273-280). American Mathematical Society.
  • Martini, Horst, Swanepoel, Konrad (2003). Generalized convexity notions and combinatorial geometry. Congressus Numerantium, 164, 65-93.
  • Swanepoel, Konrad (2003). Helly-type theorems for homothets of planar convex curves. Proceedings of the Mathematical Society, 131(3), 921-932. https://doi.org/10.1090/S0002-9939-02-06722-9
  • Martini, Horst, Swanepoel, Konrad, Weiss, G. (2003-02-27 - 2003-03-01) Some location problems in normed linear spaces [Paper]. Dresden Symposium Geometrie: konstruktiv & kinematisch, Dresden, Germany, DEU.
  • Martini, Horst, Swanepoel, Konrad, Weiss, Gunter (2002). The Fermat-Torricelli problem in normed planes and spaces. Journal of Optimization Theory and Applications, 115(2), 283-314. https://doi.org/10.1023/A:1020884004689
  • Swanepoel, Konrad (2002). Independence numbers of planar contact graphs. Discrete and Computational Geometry, 28(4), 649-670. https://doi.org/10.1007/s00454-002-2897-y
  • Swanepoel, Konrad (2002). Helly-type theorems for polygonal curves. Discrete Mathematics, 254(1-3), 527-537. https://doi.org/10.1016/S0012-365X(01)00379-X
  • Brass, Peter, Rote, Gunter, Swanepoel, Konrad (2001). Triangles of extremal area or perimeter in a finite planar point set. Discrete and Computational Geometry, 26(1), 51-58. https://doi.org/10.1007/s00454-001-0010-6
  • Martini, Horst, Swanepoel, Konrad, Weiss, Gunter (2001). The geometry of Minkowski spaces - a survey. Part I. Expositiones Mathematicae, 19(2), 97-142. https://doi.org/10.1016/S0723-0869(01)80025-6
  • Swanepoel, Konrad (2000). Sets of unit vectors with small pairwise sums. Quaestiones Mathematicae, 23(3), 383-288.
  • Swanepoel, Konrad (2000). The local Steiner problem in normed planes. Networks, 36(2), 104-113. https://doi.org/10.1002/1097-0037(200009)36:2<104::AID-NET5>3.0.CO;2-K
  • Swanepoel, Konrad (2000). Gaps in convex disc packings with an application to 1-Steiner minimum trees. Monatshefte fur Mathematik, 129(3), 217-226. https://doi.org/10.1007/s006050050072
  • Swanepoel, Konrad (2000). Balancing unit vectors. Journal of Combinatorial Theory, Series A, 89(1), 105-112. https://doi.org/10.1006/jcta.1999.3011
  • Swanepoel, Konrad (2000). On the existence of shortest directed networks. Journal of Combinatorial Mathematics and Combinatorial Computing, 33, 97-102.
  • Swanepoel, Konrad (1999). New lower bounds for the Hadwiger numbers of ℓp balls for p < 2. Applied Mathematics Letters, 12(5), 57-60. https://doi.org/10.1016/S0893-9659(99)00057-9
  • 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. https://doi.org/10.1007/PL00009431
  • 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.
  • Swanepoel, Konrad (1999). Cardinalities of k-distance sets in Minkowski spaces. Discrete Mathematics, 197/19, 759-767. https://doi.org/10.1016/S0012-365X(99)90143-7
  • Swanepoel, Konrad (1999). Helly-type theorems for hollow axis-aligned boxes. Proceedings of the Mathematical Society, 127(7), 2155-2162. https://doi.org/10.1090/S0002-9939-99-04966-7
  • Swanepoel, Konrad (1996). Extremal problems in Minkowski space related to minimal networks. Proceedings of the Mathematical Society, 124(8), 2513-2518. https://doi.org/10.1090/S0002-9939-96-03370-9
    • Public
  • Strachan, Cameron, Swanepoel, Konrad (2026). Edge isoperimetry of lattices. Annals of Combinatorics, https://doi.org/10.1007/s00026-025-00801-x picture_as_pdf
  • Kobos, Tomasz, Swanepoel, Konrad (2025). Equilateral dimension of the planar Banach-Mazur compactum. Proceedings of the American Mathematical Society, 153(10), 4423 - 4436. https://doi.org/10.1090/proc/17323 picture_as_pdf
  • Lavollée, Jérémy, Swanepoel, Konrad (2024). A tight bound for the number of edges of matchstick graphs. Discrete and Computational Geometry, 72(4), 1530 - 1544. https://doi.org/10.1007/s00454-023-00530-z picture_as_pdf
  • Lavollée, Jérémy, Swanepoel, Konrad (2023). The number of small-degree vertices in matchstick graphs. Australasian Journal of Combinatorics, 85(1), 92 - 99. picture_as_pdf
  • Naszódi, Márton, Swanepoel, Konrad J. (2022). Contacts in totally separable packings in the plane and in high dimensions. Journal of Computational Geometry, 13(1), 471 - 483. https://doi.org/10.20382/jocg.v13i1a17 picture_as_pdf
  • Lavollée, Jérémy, Swanepoel, Konrad (2022). Bounding the number of edges of matchstick graphs. SIAM Journal on Discrete Mathematics, 36(1), 777 - 785. https://doi.org/10.1137/21M1441134 picture_as_pdf
  • Swanepoel, Konrad (2021). Outer linear measure of connected sets via Steiner trees. Real Analysis Exchange, 46(1), 207 - 232. https://doi.org/10.14321/realanalexch.46.1.0207 picture_as_pdf
  • Swanepoel, Konrad (2021). Triangles of nearly equal area. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 62(1), 219 - 227. https://doi.org/10.1007/s13366-021-00567-2 picture_as_pdf
  • Lin, Aaron, Swanepoel, Konrad (2021). Ordinary hyperspheres and spherical curves. Advances in Geometry, 21(1), 15 - 22. https://doi.org/10.1515/advgeom-2020-0031 picture_as_pdf
  • Naszódi, Márton, Prokaj, Vilmos, Swanepoel, Konrad (2020). Angular measures and Birkhoff orthogonality in Minkowski planes. Aequationes Mathematicae, 94(5), 969 - 977. https://doi.org/10.1007/s00010-020-00715-4 picture_as_pdf
  • Maxwell, Alastair, Swanepoel, Konrad (2020). Shortest directed networks in the plane. Graphs and Combinatorics, 36(5), 1457 - 1475. https://doi.org/10.1007/s00373-020-02183-8 picture_as_pdf
  • Swanepoel, Konrad (2020). Favourite distances in 3-space. Electronic Journal of Combinatorics, 27(2), 1-11. https://doi.org/10.37236/8887 picture_as_pdf
  • Balko, Martin, Por, Attila, Scheucher, Manfred, Swanepoel, Konrad, Valtr, Pavel (2020). Almost-equidistant sets. Graphs and Combinatorics, 36(3), 729 - 754. https://doi.org/10.1007/s00373-020-02149-w picture_as_pdf
  • Lin, Aaron, Swanepoel, Konrad (2020). On sets defining few ordinary hyperplanes. Discrete Analysis, https://doi.org/10.19086/da.11949 picture_as_pdf
  • Frankl, Nóra, Kupavskii, Andrey, Swanepoel, Konrad (2020). Embedding graphs in Euclidean space. Journal of Combinatorial Theory, Series A, 171, https://doi.org/10.1016/j.jcta.2019.105146 picture_as_pdf
  • Lin, A, Swanepoel, Konrad (2019). Ordinary planes, coplanar quadruples, and space quartics. Journal of the London Mathematical Society, 100(3), 937-956. https://doi.org/10.1112/jlms.12251 picture_as_pdf
  • Kupavskii, Andrey, Mustafa, Nabil H., Swanepoel, Konrad (2019). Bounding the size of an almost-equidistant set in Euclidean space. Combinatorics, Probability and Computing, 28(2), 280-286. https://doi.org/10.1017/S0963548318000287
  • Naszódi, Márton, Swanepoel, Konrad (2018). Arrangements of homothets of a convex body II. Contributions to Discrete Mathematics, 13(2), 116 - 123. https://doi.org/10.11575/cdm.v13i2.62732
  • Lin, Aaron, Makhul, Mehdi, Mojarrad, Hossein Nassajian, Schicho, Josef, Swanepoel, Konrad, de Zeeuw, Frank (2018). On sets defining few ordinary circles. Discrete and Computational Geometry, 59(1), 59-87. https://doi.org/10.1007/s00454-017-9885-8
  • Ras, Charl J., Swanepoel, Konrad J., Thomas, Doreen (2017). Approximate Euclidean Steiner trees. Journal of Optimization Theory and Applications, 172(3), 845-873. https://doi.org/10.1007/s10957-016-1036-5
  • Naszódi, Márton, Pach, János, Swanepoel, Konrad (2017). Arrangements of homothets of a convex body. Mathematika, 63(2), 696 - 710. https://doi.org/10.1112/S0025579317000122
  • Swanepoel, Konrad (2016). Sets of unit vectors with small subset sums. Transactions of the American Mathematical Society, 368(10), 7153 - 7188. https://doi.org/10.1090/tran/6601
  • Brazil, Marcus, Ras, Charl J., Swanepoel, Konrad, Thomas, Doreen A. (2015). Generalised k-Steiner tree problems in normed planes. Algorithmica, 71(1), 66-86. https://doi.org/10.1007/s00453-013-9780-5
  • Pach, János, 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. https://doi.org/10.1007/s13366-014-0211-9
  • Swanepoel, Konrad J. (2014). Equilateral sets and a Schütte theorem for the 4-norm. Canadian Mathematical Bulletin, 57(3), 640-647. https://doi.org/10.4153/CMB-2013-031-0
  • Swanepoel, Konrad (2014). Book review: Beautiful geometry by Eli Maor and Eugen Jost.
  • Swanepoel, Konrad J., Villa, Rafael (2013). Maximal equilateral sets. Discrete and Computational Geometry, 50(2), 354-373. https://doi.org/10.1007/s00454-013-9523-z
    • Restricted
  • Swanepoel, Konrad (2024). Regular matchstick graphs on the sphere. American Mathematical Monthly, https://doi.org/10.1080/00029890.2025.2599752 [In Press] picture_as_pdf
  • Swanepoel, Konrad (2018). Combinatorial distance geometry in normed spaces. In Ambrus, G., Barany, I., Boroczky, K. J., Fejes Toth, G. & Pach, J. (Eds.), New Trends in Intuitive Geometry (pp. 407 - 458). Springer Berlin / Heidelberg. https://doi.org/10.1007/978-3-662-57413-3_17 picture_as_pdf
  • Naszódi, Márton, Pach, János, Swanepoel, Konrad (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). picture_as_pdf