Publications and online available papers of Imre Bárány

A short proof of Kneser's conjecture,
J. Comb. Theory A, 25 (1978), 325326.

On a common generalization of Borsuk's and Radon's
theorem,
Acta. Math. Hung., 34 (1978), 323329 (with
E.G. Bajmóczy).

On a class of balancing games,
J. Comb. Theory A, 26 (1979), 115126.

Borsuk's theorem through complementary pivoting,
Math. Programming, 18 (1980), 8488.

On a topological generalization of a theorem of
Tverberg,
J. London Math. Soc., 23 (1981),
158164 (with S.B. Shlosman and A. Szűcs).

A vectorsum theorem and its application to improving
flow shop guarantees,
Math. Op. Res., 6 (1981), 445455.

On some combinatorial questions in finite dimensional
spaces,
Lin. Alg. Appl., 19 (with V.S. Grinberg).

Systems of representatives for sets whose convex hull
contains zero,,
Algebraic methods in graph theory,
Colloquia Math. Soc. J. Bolyai 25 (1981), 1925.

A generalization of Charathéodory's theorem,
Discrete Math., 40 (1982), 141152.

Borsuk's theorem and the number of facets of centrally
symmetric polytopes,
Acta Math. Hung., 40 (1982), 323329 (with L. Lovász).

Quantitative Hellytype theorems,
Proc. Amer. Math. Soc., 86 (1982), 109114 (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
problems,
Szigma, 16 (1983), 1735 (with T.
Fiala), (in Hungarian).

Mental poker with three or more players,
Information and Control, 59 (1983), 8493 (with Z.
Füredi).

Discrete convex functions and proof of the six circle
conjecture of Fejes Tóth,
Can. J. Math., 36 (1983), 569576 (with Z. Füredi and
J. Pach).

Helly's theorem with volumes,
Amer. Math. Monthly, 78 (1984), 862365 (with
M. Katchalski and J. Pach).

Strong formulations for multiitem capacitated lot
sizing,
Management Science, 30 (1984),
12551261 (with T. van Roy and L. A. Wolsey).

Uncapacitated lotsizing: the convex hull of solutions,
Math. Programming Study, 22 (1984), 3243
(with T. van Roy and L. A. Wolsey).

A vectorsum theorem in twodimensional space,
Per. Math. Hung., 16 (1985), 569576 (with V.S.
Grinberg).

Covering all secants in a square,
in: Intuitive Geometry, Colloquia Math. Soc. J. Bolyai 48 (1985),
1927 (with Z. Füredi).

Packing and covering a tree by subtrees,
Combinatorica, 6 (1986), 135138 (with J. Edmonds and
L.A. Wolsey).

Maximal volume enclosed by plates and proof of the
chessboard conjecture,
Discrete Math., 60 (1986), 101120 (with K. Börczky,
E. Makai Jr. and J. Pach).

A characterization of the Helly dimension of convex
bodies,
Studia Math. Hung., 22 (1987), 402406
(with J. Kincses).

Covering with Euclidean boxes,
European J. Comb., 8 (1987), 113119 (with J. Lehel).

An extension of the ErdősSzekeres theorem on large
angles,
Combinatorica, 7 (1987), 161169.

Computing the volume is difficult,
Discrete and Comput. Geometry, 2 (1987), 319326, and
Proc. 18th ACMSTOC (1986), 442447 (with Z. Füredi).

Empty simplices in Euclidean space,
Can. Math. Bull., 30 (1987), 436445 (with Z. Füredi).

On the minimal ring containing the boundary of a convex
body,
Acta Math. Szeged, 52 (1988), 93100.

Approximation of the sphere by polytopes having few
vertices,
Proc. Amer. Math. Soc., 102 (1988),
651660 (with Z. Füredi).

On the shape of the convex hull of random points,
J. Prob. Theory and Appl., 77 (1988), 231240 (with
Z. Füredi).

Convex bodies, economic cap coverings, random
polytopes,
Mathematika, 35 (1988), 279291
(with D.G. Larman).

A stability property of the densest circle packing,
Monatshäfte Math., 106 (1988), 107114 (with
N.K. Dolbilin).

Rearrangement of series in infinite dimensional spaces,
Mat. Zametki, 46 (1989), 1017. (in Russian)

Intrinsic volumes and fvectors of random polytopes,
Math. Annalen, 285 (1989), 671699.

A combinatorial result about points and balls in
Euclidean space,
Discrete Comp. Geometry, 4 (1989), 259262 (with
J.H. Schmerl, S.J. Sidney and J. Urrutia).

The Carathéodory number for the kcore,
Combinatorica, 10 (1990), 185194 (with M. Perles).

A combinatorial property of points and ellipsoids,
Discrete Comp. Geometry, 5 (1990), 375382 (with
D.G. Larman).

Diameters in typical convex bodies,
Can. J. Math., 42 (1990), 5061 (with T. Zamfirescu).

On the number of halving planes,
Combinatorica, 10 (1990), 175183, and Proc. 5th Symp. Comp.
Geom., (1989), 140144 (with Z. Füredi and L. Lovász).

On affinely embeddable sets in the projective plane,
Acta Math. Hung., 56 (1990), 137141.

On the convex hull of uniform random points in an
arbitrary dpolytope,
Anz. Öster. Akad. Wiss. Math.Natur., 77 (1990), 2527 (with
C. Buchta).

On the expected number of ksets,
Proc. 2nd Can. Conf. Comp. Geom., (1990), 5559 (with
W. Steiger).

Do projections go to infinity?,
in: The Victor Klee Festschrift, (ed. P. Gritzman and B. Sturmfels),
DIMACS series no 4 (1991), 5163 (with J.E. Goodman and R.
Pollack).

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), 3944, and
Proc. 7th Symp. Comp. Geom. (1991), 162165 (with A. Balog).

Fair distribution protocols or how the players replace
fortune,
Math. Op. Res., 17 (1992), 327340.

On integer points in polyhedra: a lower bound,
Combinatorica, 12 (1992), 135142. (with R. Howe and
L. Lovász).

A coloured version of Tverberg's theorem,
J. London Math. Soc. (2) 45 (1992), 314320 (with D.G.
Larman).

On the number of convex lattice polygons,
Combinatorics, Probability, and Computation, 1 (1992), 295302
(with J. Pach).

Random polytopes in smooth convex bodies,
Mathematika, 39 (1992), 8192.

Classification of twoperson ordinal bimatrix games
,
Intern. J. Game Theory, 21 (1992),
267290 (with J. Lee and M. Shubik).

Point selections and weak εnets for convex
hulls,
Combinatorics, Probability, and Computation, 1 (1992), 189200
(with N. Alon, Z. Füredi, and D. Kleitman).

On the number of convex lattice polytopes,
Geom. Functional Analysis, 2 (1992), 381393 (with A. M.
Vershik).

Geometric and combinatorial applications of Borsuk's
theorem: a survey,
in: New trends in computational geometry
(ed. J. Pach) (1993), 235250.

Reflecting a triangle in the plane,
Graphs and Combinatorics, 9 (1993), 97104, (with
P. Frankl and H. Maehara).

Random polytopes in a convex polytope, independence of
shape, and concentration of vertices,
Math. Annalen, 297 (1993), 467497, (with C. Buchta).

Random convex hulls: floating bodies and expectations,
Approximation Theory, 75 (1993), 130135
(with R. Vitale)

On the expected number of ksets,
Discrete and Comp. Geom., 11 (1994), 243263, (with
W. Steiger ).

The complex of maximal lattice free simplices,
Math. Programming, 66 (1994), 273281, and 3rd
IPCO (1993), (with R. Howe, and H. E. Scarf).

A note on the pathdiscrepancy of trees,
Studia Math. Hung., 30 (1995), 1315, (with Gy. Károlyi).

The densest (n+2)set in R^{n},
in: Intuitive Geometry Colloquia Math. Soc. J. Bolyai, 63 (1991),
710.

On the exact constant in the quantitative Steinitz theorem
in the plane
,
Discrete and Comp. Geom., 12 (1994),
387398 (with A. Heppes).

Rich cells in an arrangement of hyperplanes,
Lin. Alg. Appl., 226228 (1995), 567575, (with H.
Bunting, D. G. Larman, J. Pach).

The limit shape of convex lattice polygons,
Discrete and Comp. Geom., 13 (1995), 279295.

Barycentric subdivision of triangles
and semigroups of Möbius maps
Mathematika, 43 (1996), 165171 (with A.F. Beardon and
T.K. Carne).

The topological structure of maximal lattice free
convex bodies: the general case,
Math. Programming Ser. A, 80 no. 1, (1998), 115. (with
H.E. Scarf and D. Shallcross), and Fourth IPCO, 1995, Copenhagen,
244252.

Carathéodory's theorem, colourful and applicable,
Bolyai Society Math. Studies, 6 Intuitive geometry, (ed.: I.
Bárány, K. Böröczky) (1997), 1122 (with S. Onn).

Colourful linear programming,
in: Integer Programming and Combinatorial Optimization, 5th IPCO proceedings,
Lecture Notes in Computer Science 1084, Springer Verlag,
1996, 115, (with S. Onn).

Affine perimeter and limit shape,
J. reine und ang. Mathematik, 484 (1997), 7184.

Colourful linear programming and its relatives,
Math. OR, 22 (1997), 550567, (with S. Onn).

Few points to generate a random polytope,
Mathematika, 44 (1997), 325331, (with L. Dalla).

Approximation by random polytopes is almost best possible,
Rendiconti di Palermo, 50 (1997), 4350.

Positive fraction ErdősSzekeres theorem,
Discr. Comp. Geometry, 19 (1998), 335342, (with
P. Valtr).

The convex hull of the integer points in a large ball,
Math. Annalen, 312 (1998), 167181, (with D.G. Larman).

Matrices with identical sets of neighbors,
Math. OR, 23 (1998), 863873, (with H.E. Scarf).

The topological structure of maximal lattice free
convex bodies: The general case,
Math. Programming, 80 (1998), 115, (with H.E. Scarf and
D. Shallcross).

Universal counting of lattice points,
Publ. de l'Institute Math. Belgrade, 66 (1999), 1722, (with
JM. Kantor).

A central limit theorem for convex chains in the square,
Discrete Comp. Geom., 23 (2000), 3550, (with G. Rote,
W. Steiger, CH. Zhang).

On the number of lattice free polytopes,
European J. Comb., 21 (2000), 103110, (with
JM. Kantor).

Sylvester's question: the probability that n points are
in convex position,
Annals of Probability, 27 (1999), 20202034.

The technique of Mregions and capcoverings: a
survey,
Rendiconti di Palermo, 65 (2000), 2138.

Simultaneous partition of measures by kfans,
Discrete Comp. Geom., 25 (2001), 317334, (with
J. Matoušek).

Covering lattice points by subspaces,
Periodica Math. Hung., 43 (2001), 93103, (with
G. Harcos, J. Pach, G. Tardos)

A note on Sylvester's fourpoint problem,
Studia Math. Hung., 38 (2001), 7377.

On the lattice diameter of a convex polygon,
Discrete Math., 241 (2001), 4150, (with Z. Füredi).

Problems and results around the ErdősSzekeres theorem,
Japanese Conference on Discrete Comp. Geometry, (2001), 91105, (with
Gy. Károlyi).

On 01 polytopes with many facets,
Advances in Math., 161 (2001), 209228,
(with A. Pór)

Equipartition of two measures by a 4fan,
Discrete Comp. Geom., 27 (2002), 293301, (with
J. Matoušek).

Random points, convex bodies, lattices,
Proceedings of the International Congress of
Mathematicians, 2002, Beijing, Vol III, 527536.

Approximation by random polytopes is of low complexity,
Rendiconti di Palermo, 70 (2002), 5356.

Integer points on the boundary of the integer hull,
in: Discrete Geometry (ed.: A. Bezdek) 2003, Marcel Dekker, New
York, 3348, (with K. Böröczky Jr.).

A fractional Helly theorem for convex lattice sets,
Advances in Math., 174 (2003), 227235, (with
J. Matoušek).

Total curvature and spiralling shortest paths,
Discrete Comp. Geom., 30 (2003), 167176, (with
K. Kuperberg and T. Zamfirescu).

Integer points in rotated convex bodies,
Discrete and Computational Geometry, 177201,
Algorithmic Combinatorics, 25 Springer, Berlin, 2003 (with
J. Matoušek).

The minimum area convex lattice ngons,
Combinatorica, 24 (2004), 171185, (with N. Tokushige).

The randomized integer hull,
Discr. Comp. Geom., 33 (2005), 325, (with J.
Matoušek)

A case when the union of polytopes is convex,
Lin. Alg. Appl., 397 (2005), 381388, (with Komei Fukuda).

Planar point sets with few empty convex polygons,
Studia Math. Hung., 41 (2004), 243266, (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
(2006), 427456.

A note on the size of the largest ball inside a convex polytope,
Periodica Math. Hung., 51 (2005), 1518,
(with Nándor Simányi).

Geometic applications of graph and hypergraph theory,
in: Combinatorial and computational geometry, (ed.: J.E. Goodman et al.)
MSRI pulications,
52 (2005) 3150 (Cambridge Univ. Press).

Nash equilibria in random games,
Proc. 46th Symposium on the Foundations
of Computer Science (FOCS), 2005, 123131, and Random Structures
and Alg., 31 (2007) 391405. (with Santosh Vempala,
Adrian Vetta).

Berge's theorem, fractional Helly, and art galleries,
Discrete Math., 306 (2006), 23032313, (with
J. Matoušek).

Balanced partitions of vector sequences,
Lin. Alg. Appl., 414 (2006), 464469, (with B. Doerr).

On maximal convex lattice polygons inscribed in a plane convex set,
Israel J. Math., 154 (2006), 337360, (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 latticepoint free: a relative of Buffon's
needle problem ,
Random Structures and Alg., 30 (2007), 414426.

Strictly convex drawings of planar graphs,
Documenta Math., 11 (2006), 369391, (with Günter Rote).

Central limit theorems for Gaussian polytopes,
Annals of Prob., 35 (2007), 15931621, (with Van H Vu).

Quadratically many colorful simplices,
SIAM J. Discrete Math., 21 (2007), 191198, (with
J. Matoušek).

Packing cones and their negatives in space,
Discrete Comp. Geom., 38 (2007), 177187, (with
J. Matoušek).

Slicing convex sets and measures by a hyperplane,
Discrete Comp. Geom., 39 (2008), 6775, (with A. Hubard,
J. Jeronimo).

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), 87103.

Random points and lattice points in convex bodies,
Bulletin of the AMS, 45 (2008), 339365.

On the power of linear dependencies,
in: Building Bridges, (ed: M. Grötschel, G.O.H
Katona), Springer, 2008, 3146.

Very Colourful theorems,
Discrete Comp. Geom., 42 (2009), 142154 (with J.
Arocha, X. Bracho, R. Fabilla, L. Montajano).

Longest convex chains,
Random Structures and Alg., (2009), 137162, (with
G. Ambrus).

Paths with no small angle,
SIAM J. Discrete Math., 23 (2009), 16551666 (with
A. Pór, P. Valtr).

Equipartitions by a convex 3fan,
Advances in Math., 223 (2010), 579593,
(with P. Blagojević, A. Szűcs).

Poisson polytopes,
Annals Prob., 38 (2010), 15071531 (with M. Reitzner).

Infinite paths with no small angle,
Mathematika, 56 (2010), 2634, (with A. Pór).

On the variance of random polytopes,
Advances in Math., 225 (2010), 19862001,
(with M. Reitzner).

Every point is critical,
Advances in Math., 235 (2013), 390397, (with JI. Ito,
A. Vilcu, T. Zamfirescu).

Intrinsic volumes of inscribed random polytopes in smooth convex bodies,
Annals of Appl. Prob., 42 (2010), 605619, (with F. Fodor,
V. Vigh).

Jarník's convex lattice ngon for nonsymmetric norms,
Math. Zeitschrift, 270 (2012), 627643, (with
N. Enriquez).

Functions, measures, and equipartitioning convex kfans,
Discrete Comp Geom., 49 (2013), 382401 (with
P. Blagojević and A. Dmitrijević Blagojević).

On the variance of random polygons,
Comp. Geom. Theory and Appl., 46 (2013), 173180, (with
W. Steiger).

Tetrahedra passing through a triangular hole, and tetrahedra fixed by a
planar frame,
Comp. Geom. Theory and Appl., 45 (2012), 1420 (with
H. Maehara and N. Tokushige).

Longest convex lattice chains in triangles,
Comp. Geom. Theory and Appl., 47 (2014), 367376 (with Edgardo Roldan Pensado).

Homogeneous selections from hyperplanes,
JCT B, 104 (2014), 8187 (with J. Pach).

On a question of V. I. Arnold,
Acta Math. Hung., 137 (2012), 7281.

Notes about the Carathéodory number ,
Discrete Comp. Geom., 48 (2012),
783792, (with Roman Karasev).

Universal points of convex bodies and bisectors in Minkowski spaces,
Advances in Geometry, 14 (2014),427445, (with R. Schneider).

Many empty triangles have a common edge,
Discrete Comp. Geom., 50 (2013),
244252, (with JF. Marckert, M. Reitzner).

A question from a famous paper of Erdős,
Discrete Comp. Geom., 50 (2013),
253261, (with E. RoldánPensado), 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), 16001601 (with B.D. Ginzburg,
V.S. Grinberg).

Holding circles and fixing frames,
Discrete Comp. Geom., (2013) (with T. Zamfirescu).

Circles holding typical convex bodies,
Libertas Mathematica, 33 (2013), 2125 (with
T. Zamfirescu).

ErdősSzekeres theorem for lines,
submitted to Discrete Comp. Geom., (2014) (with
Edgardo RoldánPensado and Géza Tóth).

Block partitions of sequences, Israel J. Math. (2014) (with V. Grinberg).

Curves in R^{d} intersecting every hyperplane at most
d+1 times,
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), 3950
(2013) (with J. JeronimoCastro).

Volumes of lattice polytopes and a question of V. I. Arnold,
Acta Math. Hung., 144 (2014), 119131 (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),
221224 (with F Fodor, L Montejano, A MartinezPerez, D Oliveros, A Por).

Antipodal coverings of spheres, accepted in the Dolbilin'70 volume
(with Ruy FabillaMonroy, and B Vogtenuber).