Publications and online available papers of Imre Bárány
A short proof of Kneser's conjecture,
J. Comb. Theory A, 25 (1978), 325-326.
On a common generalization of Borsuk's and Radon's
Acta. Math. Hung., 34 (1978), 323-329 (with
On a class of balancing games,
J. Comb. Theory A, 26 (1979), 115-126.
Borsuk's theorem through complementary pivoting,
Math. Programming, 18 (1980), 84-88.
On a topological generalization of a theorem of
J. London Math. Soc., 23 (1981),
158-164 (with S.B. Shlosman and A. Szűcs).
A vector-sum theorem and its application to improving
flow shop guarantees,
Math. Op. Res., 6 (1981), 445-455.
On some combinatorial questions in finite dimensional
Lin. Alg. Appl., 1-9 (with V.S. Grinberg).
Systems of representatives for sets whose convex hull
Algebraic methods in graph theory,
Colloquia Math. Soc. J. Bolyai 25 (1981), 19-25.
A generalization of Charathéodory's theorem,
Discrete Math., 40 (1982), 141-152.
Borsuk's theorem and the number of facets of centrally
Acta Math. Hung., 40 (1982), 323-329 (with L. Lovász).
Quantitative Helly-type theorems,
Proc. Amer. Math. Soc., 86 (1982), 109-114 (with
M. Katchalski and J. Pach).
Algorithms to compute fixed points of continuous maps,
MNIIPU Publications, Moscow (in Russian), (1983).
Near optimal solutions of multimachine scheduling
Szigma, 16 (1983), 17-35 (with T.
Fiala), (in Hungarian).
Mental poker with three or more players,
Information and Control, 59 (1983), 84-93 (with Z.
Discrete convex functions and proof of the six circle
conjecture of Fejes Tóth,
Can. J. Math., 36 (1983), 569-576 (with Z. Füredi and
Helly's theorem with volumes,
Amer. Math. Monthly, 78 (1984), 862-365 (with
M. Katchalski and J. Pach).
Strong formulations for multi-item capacitated lot
Management Science, 30 (1984),
1255-1261 (with T. van Roy and L. A. Wolsey).
Uncapacitated lot-sizing: the convex hull of solutions,
Math. Programming Study, 22 (1984), 32-43
(with T. van Roy and L. A. Wolsey).
A vector-sum theorem in two-dimensional space,
Per. Math. Hung., 16 (1985), 569-576 (with V.S.
Covering all secants in a square,
in: Intuitive Geometry, Colloquia Math. Soc. J. Bolyai 48 (1985),
19-27 (with Z. Füredi).
Packing and covering a tree by subtrees,
Combinatorica, 6 (1986), 135-138 (with J. Edmonds and
Maximal volume enclosed by plates and proof of the
Discrete Math., 60 (1986), 101-120 (with K. Börczky,
E. Makai Jr. and J. Pach).
A characterization of the Helly dimension of convex
Studia Math. Hung., 22 (1987), 402-406
(with J. Kincses).
Covering with Euclidean boxes,
European J. Comb., 8 (1987), 113-119 (with J. Lehel).
An extension of the Erdős-Szekeres theorem on large
Combinatorica, 7 (1987), 161-169.
Computing the volume is difficult,
Discrete and Comput. Geometry, 2 (1987), 319-326, and
Proc. 18th ACM-STOC (1986), 442-447 (with Z. Füredi).
Empty simplices in Euclidean space,
Can. Math. Bull., 30 (1987), 436-445 (with Z. Füredi).
On the minimal ring containing the boundary of a convex
Acta Math. Szeged, 52 (1988), 93-100.
Approximation of the sphere by polytopes having few
Proc. Amer. Math. Soc., 102 (1988),
651-660 (with Z. Füredi).
On the shape of the convex hull of random points,
J. Prob. Theory and Appl., 77 (1988), 231-240 (with
Convex bodies, economic cap coverings, random
Mathematika, 35 (1988), 279-291
(with D.G. Larman).
A stability property of the densest circle packing,
Monatshäfte Math., 106 (1988), 107-114 (with
Rearrangement of series in infinite dimensional spaces,
Mat. Zametki, 46 (1989), 10-17. (in Russian)
Intrinsic volumes and f-vectors of random polytopes,
Math. Annalen, 285 (1989), 671-699.
A combinatorial result about points and balls in
Discrete Comp. Geometry, 4 (1989), 259-262 (with
J.H. Schmerl, S.J. Sidney and J. Urrutia).
The Carathéodory number for the k-core,
Combinatorica, 10 (1990), 185-194 (with M. Perles).
A combinatorial property of points and ellipsoids,
Discrete Comp. Geometry, 5 (1990), 375-382 (with
Diameters in typical convex bodies,
Can. J. Math., 42 (1990), 50-61 (with T. Zamfirescu).
On the number of halving planes,
Combinatorica, 10 (1990), 175-183, and Proc. 5th Symp. Comp.
Geom., (1989), 140-144 (with Z. Füredi and L. Lovász).
On affinely embeddable sets in the projective plane,
Acta Math. Hung., 56 (1990), 137-141.
On the convex hull of uniform random points in an
Anz. Öster. Akad. Wiss. Math.-Natur., 77 (1990), 25-27 (with
On the expected number of k-sets,
Proc. 2nd Can. Conf. Comp. Geom., (1990), 55-59 (with
Do projections go to infinity?,
in: The Victor Klee Festschrift, (ed. P. Gritzman and B. Sturmfels),
DIMACS series no 4 (1991), 51-63 (with J.E. Goodman and R.
On the convex hull of the integer points in a disk,
in: Discrete and Computational Geometry (ed. J.E.Goodman,
R. Pollack, and W. Steiger), DIMACS Series no 6 (1991), 39-44, and
Proc. 7th Symp. Comp. Geom. (1991), 162-165 (with A. Balog).
Fair distribution protocols or how the players replace
Math. Op. Res., 17 (1992), 327-340.
On integer points in polyhedra: a lower bound,
Combinatorica, 12 (1992), 135-142. (with R. Howe and
A coloured version of Tverberg's theorem,
J. London Math. Soc. (2) 45 (1992), 314-320 (with D.G.
On the number of convex lattice polygons,
Combinatorics, Probability, and Computation, 1 (1992), 295-302
(with J. Pach).
Random polytopes in smooth convex bodies,
Mathematika, 39 (1992), 81-92.
Classification of two-person ordinal bimatrix games
Intern. J. Game Theory, 21 (1992),
267-290 (with J. Lee and M. Shubik).
Point selections and weak ε-nets for convex
Combinatorics, Probability, and Computation, 1 (1992), 189-200
(with N. Alon, Z. Füredi, and D. Kleitman).
On the number of convex lattice polytopes,
Geom. Functional Analysis, 2 (1992), 381-393 (with A. M.
Geometric and combinatorial applications of Borsuk's
theorem: a survey,
in: New trends in computational geometry
(ed. J. Pach) (1993), 235-250.
Reflecting a triangle in the plane,
Graphs and Combinatorics, 9 (1993), 97-104, (with
P. Frankl and H. Maehara).
Random polytopes in a convex polytope, independence of
shape, and concentration of vertices,
Math. Annalen, 297 (1993), 467-497, (with C. Buchta).
Random convex hulls: floating bodies and expectations,
Approximation Theory, 75 (1993), 130-135
(with R. Vitale)
On the expected number of k-sets,
Discrete and Comp. Geom., 11 (1994), 243-263, (with
W. Steiger ).
The complex of maximal lattice free simplices,
Math. Programming, 66 (1994), 273-281, and 3rd
IPCO (1993), (with R. Howe, and H. E. Scarf).
A note on the path-discrepancy of trees,
Studia Math. Hung., 30 (1995), 13-15, (with Gy. Károlyi).
The densest (n+2)-set in Rn,
in: Intuitive Geometry Colloquia Math. Soc. J. Bolyai, 63 (1991),
On the exact constant in the quantitative Steinitz theorem
in the plane
Discrete and Comp. Geom., 12 (1994),
387-398 (with A. Heppes).
Rich cells in an arrangement of hyperplanes,
Lin. Alg. Appl., 226-228 (1995), 567-575, (with H.
Bunting, D. G. Larman, J. Pach).
The limit shape of convex lattice polygons,
Discrete and Comp. Geom., 13 (1995), 279-295.
Barycentric subdivision of triangles
and semigroups of Möbius maps
Mathematika, 43 (1996), 165-171 (with A.F. Beardon and
The topological structure of maximal lattice free
convex bodies: the general case,
Math. Programming Ser. A, 80 no. 1, (1998), 1-15. (with
H.E. Scarf and D. Shallcross), and Fourth IPCO, 1995, Copenhagen,
Carathéodory's theorem, colourful and applicable,
Bolyai Society Math. Studies, 6 Intuitive geometry, (ed.: I.
Bárány, K. Böröczky) (1997), 11-22 (with S. Onn).
Colourful linear programming,
in: Integer Programming and Combinatorial Optimization, 5th IPCO proceedings,
Lecture Notes in Computer Science 1084, Springer Verlag,
1996, 1-15, (with S. Onn).
Affine perimeter and limit shape,
J. reine und ang. Mathematik, 484 (1997), 71-84.
Colourful linear programming and its relatives,
Math. OR, 22 (1997), 550-567, (with S. Onn).
Few points to generate a random polytope,
Mathematika, 44 (1997), 325-331, (with L. Dalla).
Approximation by random polytopes is almost best possible,
Rendiconti di Palermo, 50 (1997), 43-50.
Positive fraction Erdős-Szekeres theorem,
Discr. Comp. Geometry, 19 (1998), 335-342, (with
The convex hull of the integer points in a large ball,
Math. Annalen, 312 (1998), 167-181, (with D.G. Larman).
Matrices with identical sets of neighbors,
Math. OR, 23 (1998), 863-873, (with H.E. Scarf).
The topological structure of maximal lattice free
convex bodies: The general case,
Math. Programming, 80 (1998), 1-15, (with H.E. Scarf and
Universal counting of lattice points,
Publ. de l'Institute Math. Belgrade, 66 (1999), 17-22, (with
A central limit theorem for convex chains in the square,
Discrete Comp. Geom., 23 (2000), 35-50, (with G. Rote,
W. Steiger, C-H. Zhang).
On the number of lattice free polytopes,
European J. Comb., 21 (2000), 103-110, (with
Sylvester's question: the probability that n points are
in convex position,
Annals of Probability, 27 (1999), 2020-2034.
The technique of M-regions and cap-coverings: a
Rendiconti di Palermo, 65 (2000), 21-38.
Simultaneous partition of measures by k-fans,
Discrete Comp. Geom., 25 (2001), 317-334, (with
Covering lattice points by subspaces,
Periodica Math. Hung., 43 (2001), 93-103, (with
G. Harcos, J. Pach, G. Tardos)
A note on Sylvester's four-point problem,
Studia Math. Hung., 38 (2001), 73-77.
On the lattice diameter of a convex polygon,
Discrete Math., 241 (2001), 41-50, (with Z. Füredi).
Problems and results around the Erdős-Szekeres theorem,
Japanese Conference on Discrete Comp. Geometry, (2001), 91-105, (with
On 0-1 polytopes with many facets,
Advances in Math., 161 (2001), 209-228,
(with A. Pór)
Equipartition of two measures by a 4-fan,
Discrete Comp. Geom., 27 (2002), 293-301, (with
Random points, convex bodies, lattices,
Proceedings of the International Congress of
Mathematicians, 2002, Beijing, Vol III, 527-536.
Approximation by random polytopes is of low complexity,
Rendiconti di Palermo, 70 (2002), 53-56.
Integer points on the boundary of the integer hull,
in: Discrete Geometry (ed.: A. Bezdek) 2003, Marcel Dekker, New
York, 33-48, (with K. Böröczky Jr.).
A fractional Helly theorem for convex lattice sets,
Advances in Math., 174 (2003), 227-235, (with
Total curvature and spiralling shortest paths,
Discrete Comp. Geom., 30 (2003), 167-176, (with
K. Kuperberg and T. Zamfirescu).
Integer points in rotated convex bodies,
Discrete and Computational Geometry, 177-201,
Algorithmic Combinatorics, 25 Springer, Berlin, 2003 (with
The minimum area convex lattice n-gons,
Combinatorica, 24 (2004), 171-185, (with N. Tokushige).
The randomized integer hull,
Discr. Comp. Geom., 33 (2005), 3-25, (with J.
A case when the union of polytopes is convex,
Lin. Alg. Appl., 397 (2005), 381-388, (with Komei Fukuda).
Planar point sets with few empty convex polygons,
Studia Math. Hung., 41 (2004), 243-266, (with P. Valtr).
Discrete and convex geometry,
in: A Panorama of Hungarian Mathematics in the Twentieth Century, (ed.:
J. Horváth), Bolyai Society Mathematical Studies 14
A note on the size of the largest ball inside a convex polytope,
Periodica Math. Hung., 51 (2005), 15-18,
(with Nándor Simányi).
Geometic applications of graph and hypergraph theory,
in: Combinatorial and computational geometry, (ed.: J.E. Goodman et al.)
52 (2005) 31-50 (Cambridge Univ. Press).
Nash equilibria in random games,
Proc. 46th Symposium on the Foundations
of Computer Science (FOCS), 2005, 123-131, and Random Structures
and Alg., 31 (2007) 391-405. (with Santosh Vempala,
Berge's theorem, fractional Helly, and art galleries,
Discrete Math., 306 (2006), 2303-2313, (with
Balanced partitions of vector sequences,
Lin. Alg. Appl., 414 (2006), 464-469, (with B. Doerr).
On maximal convex lattice polygons inscribed in a plane convex set,
Israel J. Math., 154 (2006), 337-360, (with M. Prodromou).
Random polytopes, convex bodies, and approximation,
Chapter in Stochastic Geometry, (ed. W. Weil), Springer, Lecture Notes
in Mathematics 1892 2007.
The chance that a convex body is lattice-point free: a relative of Buffon's
needle problem ,
Random Structures and Alg., 30 (2007), 414-426.
Strictly convex drawings of planar graphs,
Documenta Math., 11 (2006), 369-391, (with Günter Rote).
Central limit theorems for Gaussian polytopes,
Annals of Prob., 35 (2007), 1593-1621, (with Van H Vu).
Quadratically many colorful simplices,
SIAM J. Discrete Math., 21 (2007), 191-198, (with
Packing cones and their negatives in space,
Discrete Comp. Geom., 38 (2007), 177-187, (with
Slicing convex sets and measures by a hyperplane,
Discrete Comp. Geom., 39 (2008), 67-75, (with A. Hubard,
Extremal problems for convex lattice polytopes: a survey,
in: Contemporary Mathematics 453,
Surveys on Discrete and Comp. Geometry, (Ed.: J.E. Gooodman et al. AMS,
Providence, RI (2008), 87-103.
Random points and lattice points in convex bodies,
Bulletin of the AMS, 45 (2008), 339-365.
On the power of linear dependencies,
in: Building Bridges, (ed: M. Grötschel, G.O.H
Katona), Springer, 2008, 31-46.
Very Colourful theorems,
Discrete Comp. Geom., 42 (2009), 142-154 (with J.
Arocha, X. Bracho, R. Fabilla, L. Montajano).
Longest convex chains,
Random Structures and Alg., (2009), 137-162, (with
Paths with no small angle,
SIAM J. Discrete Math., 23 (2009), 1655-1666 (with
A. Pór, P. Valtr).
Equipartitions by a convex 3-fan,
Advances in Math., 223 (2010), 579-593,
(with P. Blagojević, A. Szűcs).
Annals Prob., 38 (2010), 1507-1531 (with M. Reitzner).
Infinite paths with no small angle,
Mathematika, 56 (2010), 26-34, (with A. Pór).
On the variance of random polytopes,
Advances in Math., 225 (2010), 1986-2001,
(with M. Reitzner).
Every point is critical,
Advances in Math., 235 (2013), 390-397, (with J-I. Ito,
A. Vilcu, T. Zamfirescu).
Intrinsic volumes of inscribed random polytopes in smooth convex bodies,
Annals of Appl. Prob., 42 (2010), 605-619, (with F. Fodor,
Jarník's convex lattice n-gon for non-symmetric norms,
Math. Zeitschrift, 270 (2012), 627-643, (with
Functions, measures, and equipartitioning convex k-fans,
Discrete Comp Geom., 49 (2013), 382-401 (with
P. Blagojević and A. Dmitrijević Blagojević).
On the variance of random polygons,
Comp. Geom. Theory and Appl., 46 (2013), 173-180, (with
Tetrahedra passing through a triangular hole, and tetrahedra fixed by a
Comp. Geom. Theory and Appl., 45 (2012), 14-20 (with
H. Maehara and N. Tokushige).
Longest convex lattice chains in triangles,
Comp. Geom. Theory and Appl., 47 (2014), 367-376 (with Edgardo Roldan Pensado).
Homogeneous selections from hyperplanes,
JCT B, 104 (2014), 81-87 (with J. Pach).
On a question of V. I. Arnold,
Acta Math. Hung., 137 (2012), 72-81.
Notes about the Carathéodory number ,
Discrete Comp. Geom., 48 (2012),
783-792, (with Roman Karasev).
Universal points of convex bodies and bisectors in Minkowski spaces,
to appear Advances in Geometry, (with R. Schneider).
Many empty triangles have a common edge,
Discrete Comp. Geom., 50 (2013),
244-252, (with J-F. Marckert, M. Reitzner).
A question from a famous paper of Erdős,
Discrete Comp. Geom., 50 (2013),
253-261, (with E. Roldán-Pensado), also appears in SoCG'2013,
Rio de Janeiro.
Tensors, colours, octahedra,
accepted, in the Pisa volume, 2012.
Colourful and fractional (p,q)-theorems,
accepted in Discrete Comp. Geom., (2013) (with F. Fodor,
L. Montejano, D. Oliveros, A. Pór).
2013 unit vectors in the plane,
Discrete Math., 313 (2013), 1600-1601 (with B.D. Ginzburg,
Holding circles and fixing frames,
Discrete Comp. Geom., (2013) (with T. Zamfirescu).
Circles holding typical convex bodies,
Libertas Mathematica, 33 (2013), 21-25 (with
Erdős-Szekeres theorem for lines,
submitted to Discrete Comp. Geom., (2014) (with
Edgardo Roldán-Pensado and Géza Tóth).
Block partitions of sequences, Israel J. Math. (2014) (with V. Grinberg).
Curves in Rd intersecting every hyperplane at most
submitted to JEMS, (2013) (with J. Matoušek).
Topology of geometric join, 1309.0920arXive (2013) (with A. Holmsen
and R. Karasev).
Helly type theorems for the sum of unit vectors, Lin. Alg. Appl., 469 (2015), 39-50
(2013) (with J. Jeronimo-Castro).
Volumes of lattice polytopes and a question of V. I. Arnold,
Acta Math. Hung., 144 (2014), 119-131 (with Liping Yuan).
Magic mirrors, dense diameteres, Baire category, submitted to J Convex Anal.,
(2014) (with M. Laczkovich).
Affine diameters of convex bodies, submitted to Proc. AMS,
(2014) (with D. Hug and R. Schneider).
Typical curvature behaviour of bodies of constant width, Advances in Math.,
(2014) (with R Schneider).
Fractional Helly for boxes in R^d, Comp. Geom. Theory Appl., 48 (2015),
221-224 (with F Fodor, L Montejano, A Martinez-Perez, D Oliveros, A Por).
Antipodal coverings of spheres, accepted in the Dolbilin'70 volume
(with Ruy Fabilla-Monroy, and B Vogtenuber).