Contact » Karoly Bezdek

Karoly Bezdek

Professor
Tier l CRC-Comp Discrete Geom

Director - Centre for Computational & Discrete Geometry
Pure Mathematics

+1 (403) 220-6919

Mathematical Sciences 318

Websites:

Research Interests

Combinatorics, Geometry and Logic:

General:

Computational Discrete Geometry:

Discrete Geometry

Currently Teaching

Not currently teaching any courses.

view past courses

Academic Positions

Canada Research Chair (Tier 1) in Computational and Discrete Geometry, Director of CCDG, Professor

Editor-in-Chief

Contributions to Discrete Mathematics

Supervision at U of C (2003 to present)

Ph.D. students: Marton Naszodi (2003-2007), Peter Papez (2003-2009), Zsolt Langi (2004-2008), Mate Salat (2009), Ryan Trelford (2009-)

M.Sc. students: Bouchra Sabbagh (2005-2007), Wes Maciejewski (2006-2007), Victoria Labute (2011-)

NSERC USRA students: Samuel Reid (May-August, 2012)

Publications

Book

Bezdek, Karoly. Lectures on Sphere Arrangements - the Discrete Geometric Side Fields Institute Monographs, Springer, New York, 2013. 192. Print.
Bezdek, Karoly, Deza, Antoine and Ye, Yinyu (Eds.). Discrete Geometry and Optimization Fields Institute Communications, Springer, New York, 2013. 336. Print.
Bezdek, Karoly. Classical Topics in Discrete Geometry CMS Books in Mathematics, Springer, New York, 2010. 166. Print.

Book Chapter

Bezdek, Karoly. "Sphere packings in 3-space" Proceedings of the COE Workshop on Sphere Packings, Kyushu University Press, 2004. 32-49. Print.
Bezdek, Karoly, Naszodi, Marton and Visy, Balazs. "On the {$m$}th {P}etty numbers of normed spaces" Discrete geometry 253. Dekker, 2003. 291-304. Print.
Bezdek, Karoly and Connelly, Robert. "The minimum mean with translation cover for sets of diameter one" 107 Jahre Drehfluchtprinzip (Vorau, 1997) Tech. Univ. Graz, 1999. 4-10. Print.
Bezdek, Karoly and Hausel, T.. "On the number of lattice hyperplanes which are needed to cover the lattice points of a convex body" Intuitive geometry (Szeged, 1991) 63. North-Holland, 1994. 27-31. Print.
Bezdek, Karoly and Zamfirescu, T.. "A characterization of {$3$}-dimensional convex sets with an infinite {X}-ray number" Intuitive geometry (Szeged, 1991) 63. North-Holland, 1994. 33-38. Print.
Beutelspacher, A. and Bezdek, Karoly. "The {H}elly dimension relative to a lattice" Intuitive geometry (Szeged, 1991) 63. North-Holland, 1994. 11-16. Print.
Bezdek, Karoly. "Hadwiger-{L}evi's covering problem revisited" New trends in discrete and computational geometry 10. Springer, 1993. 199-233. Print.
Bezdek, Karoly. "On planar tilings with finitely many sorts of tiles" Topics in combinatorics and graph theory (Oberwolfach, 1990) Physica, 1990. 79-85. Print.
Bezdek, Karoly, Connelly, R. and Kertesz, G.. "On the average number of neighbors in a spherical packing of congruent circles" Intuitive geometry (Si\'ofok, 1985) 48. North-Holland, 1987. 37-52. Print.

Conference Proceedings

Forthcoming

Bezdek, Karoly. Tarski's plank problem revisited "Bolyai Soc. Math. Studies, Springer" (to appear)

Journal Article

Bezdek, Karoly. "On a strong version of the Kepler conjecture". Mathematika 59.1 (2013): 23-30. Print.
Bezdek, Karoly and Naszodi, Marton. "Rigid ball-polyhedra in Euclidean 3-space". Discrete Comput. Geom. 49.2 (2013): 189-199. Print.
Bezdek, Karoly and Reid, Samuel. "Contact graphs of unit sphere packings revisited". J. Geom. 104.1 (2013): 57-83. Print.
Bezdek, Karoly. "Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width". Discrete and Computational Geometry 47.2 (2012): 275-287. Print.
Bezdek, Karoly. "Contact numbers for congruent sphere packings in Euclidean 3-space". Discrete and Computational Geometry 48.2 (2012): 298–309. Print.
Bezdek, Karoly. "The illumination conjecture for spindle convex bodies". Proceedings of the Steklov Institute of Mathematics 275.1 (2011): 169–176. Print.
Bezdek, Karoly and Schneider, Rolf. "Covering large balls with convex sets in spherical space". Beiträge zur Algebra und Geometrie 51.1 (2010): 229-235. Print.
Bezdek, Karoly and Kiss, Gyorgy. "On the X-ray number of almost smooth convex bodies and of convex bodies of constant width". Canadian Mathematical Bulletin 52.3 (2009): 342-348. Print.
Bezdek, Karoly and Litvak, Alexander. "Covering convex bodies by cylinders and lattice points by flats". Journal of Geometric Analysis 19.2 (2009): 233-243. Print.
Bezdek, Karoly and Bezdek, Daniel. "Shortest billiard trajectories". Geometriae Dedicata 141.1 (2009): 197-206. Print.
Bezdek, Karoly. "From the Kneser-Poulsen conjecture to ball-polyhedra". European Journal of Combinatorics 29.8 (2008): 1820-1830. Print.
Bezdek, Karoly and Connelly, Robert. "On the weighted Kneser-Poulsen conjecture". Periodica Mathematica Hungarica 57.2 (2008): 121-129. Print.
Bezdek, Karoly and Litvak, Alexander. "On the vertex index of convex bodies". Advances in Mathematics 215.2 (2007): 626-641. Print.
Bezdek, Karoly, Langi, Zsolt, Naszodi, Marton and Papez, Peter. "Ball-polyhedra". Discrete and Computational Geometry 38.2 (2007): 201-230. Print.
Bezdek, Karoly, Connelly, Robert and Csikos, Balazs. "On the perimeter of the intersection of congruent disks". Beitrage zur Algebra und Geometrie. Contributions to Algebra and Geometry 47.1 (2006): 53-62. Print.
Bezdek, Karoly and Naszodi, Marton. "Rigidity of ball-polyhedra in Euclidean 3-space". European Journal of Combinatorics 27.2 (2006): 255-268. Print.
Bezdek, Karoly. "Sphere Packings Revisited". European Journal of Combinatorics 27.6 (2006): 864-883. Print.
Bezdek, Karoly, Bisztriczky, Ted, Csikos, Balazs and Heppes, Aladar. "On the transversal Helly numbers of disjoint and overlapping disks". Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 87.1 (2006): 86-96. Print.
Bezdek, Karoly. "The illumination conjecture and its extensions". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 53.1-2 (2006): 59-69. Print.
Bezdek, Karoly, Boroczky, Karoly and Kiss, Gyorgy. "On the successive illumination parameters of convex bodies". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 53.1-2 (2006): 71-82. Print.
Bezdek, Karoly, Naszodi, Marton and Oliveros-Braniff, Deborah. "Antipodality in hyperbolic space". Journal of Geometry 85. (2006): 22-31. Print.
Bezdek, Karoly, Bisztriczky, Ted and Boroczky, Karoly. "Edge-antipodal 3-polytopes". Combinatorial and Computational Geometry, MSRI Publications 52. (2005): 129-134. Print.
Bezdek, Karoly. "Finding the best face on a Voronoi polyhedron - the strong dodecahedral conjecture revisited". Monatshefte fur Mathematik 145. (2005): 191-206. Print.
Bezdek, Karoly. "On the monotonicity of the volume of hyperbolic convex polyhedra". Beitrage zur Algebra und Geometrie. Contributions to Algebra and Geometry 46.2 (2005): 609-614. Print.
Bezdek, Karoly and Connelly, Robert. "The Kneser-Poulsen Conjecture for Spherical Polytopes". Discrete and Computational Geometry 32.1 (2004): 101-106. Print.
Bezdek, Karoly. "On {$k\sp +$}-neighbour packings and one-sided {H}adwiger configurations". Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 44.2 (2003): 493-498. Print.
Bezdek, Karoly. "The {R}adon number of the three-dimensional integer lattice". Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 30.2 (2003): 181-184. Print.
Bezdek, Karoly. "On the maximum number of touching pairs in a finite packing of translates of a convex body". Journal of Combinatorial Theory. Series A 98.1 (2002): 192-200. Print.
Bezdek, Karoly. "Improving {R}ogers' upper bound for the density of unit ball packings via estimating the surface area of {V}oronoi cells from below in {E}uclidean {$d$}-space for all {$d\ge8$}". Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 28.1 (2002): 75-106. Print.
Bezdek, Karoly. "Pushing disks apart-the {K}neser-{P}oulsen conjecture in the plane". Journal f\"ur die Reine und Angewandte Mathematik 553. (2002): 221-236. Print.
Bezdek, Karoly. "The polyhedral {T}ammes problem". Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 76.4 (2001): 314-320. Print.
Bezdek, Karoly. "On rhombic dodecahedra". Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 41.2 (2000): 411-416. Print.
Bezdek, Karoly. "On a stronger form of {R}ogers's lemma and the minimum surface area of {V}oronoi cells in unit ball packings". Journal f\"ur die Reine und Angewandte Mathematik 518. (2000): 131-143. Print.
Bezdek, Karoly. "A lower bound for the mean width of {V}oronoi polyhedra of unit ball packings in {$\bold E\sp 3$}". Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 74.5 (2000): 392-400. Print.
Bezdek, Karoly. "Two-distance preserving functions from {E}uclidean space". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 185-200. Print.
Bezdek, Karoly and Langi, Zsolt. "Almost equidistant points on {$S\sp {d-1}$}". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 139-144. Print.
Bezdek, Karoly. "Voronoi polyhedra of unit ball packings with small surface area". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 107-118. Print.
Bezdek, Karoly. "Danzer-{G}r\"unbaum's theorem revisited". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 39.1-3 (1999): 7-15. Print.
Bezdek, Karoly. "The minimum mean width translation cover for sets of diameter one". Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 39.2 (1998): 473-479. Print.
Bezdek, A. and Bezdek, Karoly. "Finite and uniform stability of sphere packings". Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 20.1 (1998): 111-130. Print.
Bezdek, Karoly and Bisztriczky, Ted. "A proof of {H}adwiger's covering conjecture for dual cyclic polytopes". Geometriae Dedicata 68.1 (1997): 29-41. Print.
Bezdek, Karoly. "Isoperimetric inequalities and the dodecahedral conjecture". International Journal of Mathematics 8.6 (1997): 759-780. Print.
Bezdek, Karoly. "Light-sources that illuminate the boundary points all but the vertices of a convex polyhedron". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 34.1-2 (1997): 17-21. Print.
Bezdek, Karoly. "Minimal translation covers for sets of diameter 1". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 34.1-2 (1997): 23-27. Print.
Bezdek, A. and Bezdek, Karoly. "Conway's fried potato problem revisited". Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 66.6 (1996): 522-528. Print.
Bezdek, Karoly. "Kepler's conjecture and the dodecahedral conjecture". Mitteilungen der DMV, Bulletin of the German Mathematical Society 96.4 (1996): 52-54. Print.
Bezdek, A. and Bezdek, Karoly. "A solution of {C}onway's fried potato problem". The Bulletin of the London Mathematical Society 27.5 (1995): 492-496. Print.
Bezdek, A. and Bezdek, Karoly. "Finite and uniform stability of sphere coverings". Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science 13.3-4 (1995): 313-319. Print.
Bezdek, Karoly and Hausel, T.. "Coating by cubes". Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 35.1 (1994): 119-123. Print.
Bezdek, Karoly, Brass, Peter and Harborth, Heiko. "Maximum convex hulls of connected systems of segments and of polyominoes". Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 35.1 (1994): 37-43. Print.
Bezdek, Karoly. "On affine subspaces that illuminate a convex set". Beitr\"age zur Algebra und Geometrie. Contributions to Algebra and Geometry 35.1 (1994): 131-139. Print.
Bezdek, Karoly. "An illumination problem for zonoids". Israel Journal of Mathematics 81.3 (1993): 265-272. Print.
Bezdek, Karoly. "A note on the illumination of convex bodies". Geometriae Dedicata 45.1 (1993): 89-91. Print.
Bezdek, Karoly and Bisztriczky, Ted. "Hadwiger's covering conjecture and low-dimensional dual cyclic polytopes". Geometriae Dedicata 46.3 (1993): 279-286. Print.
Bezdek, Karoly, Ladvanszky, Janos and Zoller, Vilmos. "The {E}uler line revisited". Elemente der Mathematik. Eine Zeitschrift der Schweizerischen Mathematischen Gesellschaft. Une Revue de la Soci\'et\'e Math\'ematique Suisse. Una Rivista della Societ\`a Matematica Svizzera 48.2 (1993): 76-79. Print.
Bezdek, Karoly. "On the illumination of unbounded closed convex sets". Israel Journal of Mathematics 80.1-2 (1992): 87-96. Print.
Bezdek, A., Bezdek, Karoly and Bisztriczky, Ted. "On illumination in the plane by line segments". Geometriae Dedicata 41.1 (1992): 39-50. Print.
Bezdek, Karoly. "Hadwiger's covering conjecture and its relatives". The American Mathematical Monthly 99.10 (1992): 954-956. Print.
Bezdek, Karoly. "On the illumination of smooth convex bodies". Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 58.6 (1992): 611-614. Print.
Bezdek, Karoly. "Research Problem 48". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 24.2 (1992): 122-123. Print.
Bezdek, Karoly. "Research Problem 47". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 24.2 (1992): 121. Print.
Bezdek, Karoly. "Research Problem 46". Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society 24.2 (1992): 119-121. Print.
Bezdek, A., Bezdek, Karoly and Bisztriczky, Ted. "On the {$(n-2)$}-transversals of {$n$} convex subsets of the plane". Geometriae Dedicata 40.3 (1991): 263-268. Print.
Bezdek, Karoly. "The problem of illumination of the boundary of a convex body by affine subspaces". Mathematika. A Journal of Pure and Applied Mathematics 38.2 (1991): 362-375 (1992). Print.
Bezdek, Karoly. "Lower bounds for packing densities". Acta Mathematica Hungarica 57.3-4 (1991): 291-311. Print.
Bezdek, A. and Bezdek, Karoly. "Interior points of the convex hull of few points in {${\bf E}\sp d$}". Monatshefte f\"ur Mathematik 111.3 (1991): 181-186. Print.
Bezdek, Karoly. "On certain translation covers". Note di Matematica 10.2 (1990): 279-286. Print.
Bezdek, Karoly and Bisztriczky, Ted. "On hyperplanes and polytopes". Monatshefte f\"ur Mathematik 109.1 (1990): 39-48. Print.
Bezdek, A. and Bezdek, Karoly. "Facets with fewest vertices". Monatshefte f\"ur Mathematik 109.2 (1990): 89-96. Print.
Bezdek, Karoly. "On billiard arcs". Beitr\"age zur Algebra und Geometrie, 30 (1990): 155-166. Print.
Bezdek, Andras and Bezdek, Karoly. "On the second smallest distance between finitely many points on the sphere". Geometriae Dedicata 29.2 (1989): 141-152. Print.
Bezdek, Karoly. "Covering curves by translates of a convex set". The American Mathematical Monthly 96.9 (1989): 789-806. Print.
Bezdek, Karoly and Schmitz, Michael. "Zur {Z}erlegung von {E}inheitskugel\"uberdeckungen des {$E\sp d$} in {E}inheitskugelpackungen". Beitr\"age zur Algebra und Geometrie, 28 (1989): 65-82. Print.
Bezdek, Andras and Bezdek, Karoly. "Polygonal cycles with a large number of components". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 32. (1989): 209-214. Print.
Bezdek, A. and Bezdek, Karoly. "On a discrete {D}ido-type question". Elemente der Mathematik. Revue de Math\'ematiques \'El\'ementaires. Rivista de Matematica Elementare 44.4 (1989): 92-100. Print.
Bezdek, A. and Bezdek, Karoly. "A note on the ten-neighbour packings of equal balls". Beitr\"age zur Algebra und Geometrie, 27 (1988): 49-53. Print.
Bezdek, Karoly and Connelly, R.. "Intersection points". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 31. (1988): 115-127. Print.
Bezdek, Karoly. "The thinnest holding-lattice of a set". Monatshefte f\"ur Mathematik 103.3 (1987): 177-185. Print.
Bezdek, Karoly. "Compact packings in the {E}uclidean space". Beitr\"age zur Algebra und Geometrie, 25 (1987): 79-84. Print.
Bezdek, A. and Bezdek, Karoly. "On the centroids of convex solids of revolution". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 30. (1987): 115-119. Print.
Bezdek, Karoly. "Densest packing of small number of congruent spheres in polyhedra". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 30. (1987): 177-194. Print.
Bezdek, Karoly. "Circle packings into convex domains of the {E}uclidean and hyperbolic plane and the sphere". Geometriae Dedicata 21.3 (1986): 249-255. Print.
Bezdek, Karoly. "Ionpackings in the space". Beitr\"age zur Algebra und Geometrie, 22 (1986): 81-88. Print.
Bezdek, Karoly. "A remark about the directed line-elements in the plane". Beitr\"age zur Algebra und Geometrie, 22 (1986): 89-94. Print.
Bezdek, Karoly. "On a {D}ido-type question". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 29. (1986): 241-244. Print.
Bezdek, A., Bezdek, Karoly and Boroczky, K.. "On compact packings". Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 21.3-4 (1986): 343-346. Print.
Bezdek, A. and Bezdek, Karoly. "When is it possible to translate a convex polyhedron in an other one?". Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 21.3-4 (1986): 337-342. Print.
Bezdek, A. and Bezdek, Karoly. "Enclosing a set by sets". Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 21.3-4 (1986): 409-413. Print.
Bezdek, A. and Bezdek, Karoly. "\"{U}ber einige d\"unnste {K}reis\"uberdeckungen konvexer {B}ereiche durch endliche {A}nzahl von kongruenten {K}reisen". Beitr\"age zur Algebra und Geometrie, 19 (1985): 159-168. Print.
Bezdek, Karoly and Joo, Istvan. "Stufenkonvexit\"at". Beitr\"age zur Algebra und Geometrie, 19 (1985): 169-175. Print.
Bezdek, Karoly. "\"{U}ber einige optimale Konfigurationen von Kreisen". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 27. (1985): 143-151. Print.
Bezdek, Karoly. "Ausf\"ullungen in der hyperbolischen Ebene durch endliche Anzahl kongruenter Kreise". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 27. (1985): 113-124. Print.
Bezdek, Karoly. "Ein elementarer {B}eweis f\"ur die isoperimetrische Ungleichung in der euklidischen und hyperbolischen Ebene". Annales Universitatis Scientiarum Budapestinensis de Rolando E\"otv\"os Nominatae. Sectio Mathematica 27. (1985): 107-112. Print.
Bezdek, Karoly and Pach, J. "A point set everywhere dense in the plane". Elemente der Mathematik. Revue de Math\'ematiques \'El\'ementaires. Rivista de Matematica Elementare 40.4 (1985): 81-84. Print.
Bezdek, Andras and Bezdek, Karoly. "Eine hinreichende {B}edingung f\"ur die \"{U}berdeckung des {E}inheitsw\"urfels durch homothetische {E}xemplare im {$n$}-dimensionalen euklidischen {R}aum". Beitr\"age zur Algebra und Geometrie, 17 (1984): 5-21. Print.
Bezdek, Karoly. "\"{U}ber einige {K}reis\"uberdeckungen". Beitr\"age zur Algebra und Geometrie, 14 (1983): 7-13. Print.
Bezdek, Karoly. "\"{U}ber {I}onenpackungen". Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 18.2-4 (1983): 277-285. Print.
Bezdek, Karoly. "Ausf\"ullung eines {K}reises durch kongruente {K}reise in der hyperbolischen {E}bene". Studia Scientiarum Mathematicarum Hungarica. A Quarterly of the Hungarian Academy of Sciences 17.1-4 (1982): 353-366. Print.
Bezdek, Karoly. "Mosaics with each face having the same number of neighbors". Mat. Lapok 28.4 (1977/80): 297-303. Print.

Other

Bezdek, Karoly. Combinatorial Geometry by Janos Pach and Pankaj K. Agarwal 35.4 1998. 341-342.

$Photograph of Karoly Bezdek$

Research Groups

Center for Computational and Discrete Geometry (CCDG)

Degrees

Awards

2010 - Canada Research Chair - Tier 1 - NSERC
2003 - Canada Research Chair - Tier 1 - NSERC
1998 - Szechenyi Professor - Hungarian government

Students

$Photograph of Ryan Trelford$ Ryan Trelford
2009 to Present

$Photograph of Victoria Labute$ Victoria Labute
2011 to Present

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