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53. On the upper chromatic number and multiple blocking sets of PG(n,q).

Author

Blázsik, Zoltán L., Héger, Tamás, and Szőnyi, Tamás

Subjects
PROJECTIVE spaces, FINITE geometries, COLORS
Abstract

We investigate the upper chromatic number of the hypergraph formed by the points and the k‐dimensional subspaces of PG(n,q); that is, the most number of colors that can be used to color the points so that every k‐subspace contains at least two points of the same color. Clearly, if one colors the points of a double blocking set with the same color, the rest of the points may get mutually distinct colors. This gives a trivial lower bound, and we prove that it is sharp in many cases. Due to this relation with double blocking sets, we also prove that for t≤38p+1, a small t‐fold (weighted) (n−k)‐blocking set of PG(n,p),p prime, must contain the weighted sum of t not necessarily distinct (n−k)‐spaces. [ABSTRACT FROM AUTHOR]

Published
2020
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64. Affinely regular polygons in an affine plane

Author

Korchmáros, Gábor and Szőnyi, Tamás

Subjects
Computer Science::Computational Geometry
Abstract

In this paper we survey results about affinely regular polygons. First, the definitions and classification of affinely regular polygons are given. Then the theory of Bachmann-Schmidt is outlined. There are several classical theorems about regular polygons, some of them having analogues in finite planes, such as the Napoleon-Barlotti theorem. Such analogues, variants of classical theorems are also collected. Affinely regular polygons occur in many combinatorial problems for sets in a finite plane. Some of these results about sharply focused arcs, internal and external nuclei, complete arcs are collected. Finally, bounds on the number of chords of an affinely regular polygon through a point are discussed., Contributions to Discrete Mathematics, Vol 3, No 1 (2008)

Published
2008
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65. Preface

Author

Korchmáros, Gábor and Szőnyi, Tamás

Abstract

Contributions to Discrete Mathematics, Vol 3, No 1 (2008)

Published
2008
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66. Directions in $\mathsf{AG}(2,p^2)$

Author

Gács, András, Lovász, László, and Szőnyi, Tamás

Subjects
affine planes, directions, blocking sets of Rédei type, 51E21
Abstract

In this paper we prove that if [math] is the square of a prime and [math] is a set of [math] points determining at least [math] directions, then either [math] is affinely equivalent to the graph of the function [math] or it determines at least [math] directions. This is sharp, the example is due to Polverino, Szőnyi and Weiner. Our method combines the lacunary polynomial and the double power sum approach.

Published
2007

78. Small point sets of PG( n, p) intersecting each line in 1 mod p points.

Author

Harrach, Nóra, Metsch, Klaus, Szőnyi, Tamás, and Weiner, Zsuzsa

Subjects
FINITE geometries, LOGICAL prediction, BLOCKING sets, COMBINATORIAL geometry, SOLID geometry, COMBINATORICS, DISCRETE geometry
Abstract

The main result of this paper is that point sets of PG( n, q), q = p, p ≥ 7 prime, of size < 3( q + 1)/2 intersecting each line in 1 modulo $${\sqrt[3] q}$$ points (these are always small minimal blocking sets with respect to lines) are linear blocking sets. As a consequence, we get that minimal blocking sets of PG( n, p), p ≥ 7 prime, of size < 3( p + 1)/2 with respect to lines are always linear. [ABSTRACT FROM AUTHOR]

Published
2010
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83. Coloring Uniform Hypergraphs with Small Edge Degrees

Author

Kostochka, Alexandr V., Rödl, Vojtěch, Kumbhat, Mohit, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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84. Rigid and Globally Rigid Graphs with Pinned Vertices

Author

Jordán, Tibor, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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85. Tight Bounds for Embedding Bounded Degree Trees

Author

Csaba, Béla, Nagy-György, Judit, Levitt, Ian, Szemerédi, Endre, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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86. Noise Sensitivity and Chaos in Social Choice Theory

Author

Kalai, Gil, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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87. Solution of Peter Winkler’s Pizza Problem*†

Author

Cibulka, Josef, Stolař, Rudolf, Kynčl, Jan, Mészáros, Viola, Valtr, Pavel, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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88. Betti Numbers are Testable*

Author

Elek, Gábor, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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89. Iterated Triangle Partitions

Author

Butler, Steve, Graham, Ron, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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90. PageRank and Random Walks on Graphs

Author

Chung, Fan, Zhao, Wenbo, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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91. High Degree Graphs Contain Large-Star Factors

Author

Alon, Noga, Wormald, Nicholas, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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93. List Total Weighting of Graphs

Author

Wong, Tsai-Lien, Zhu, Xuding, Yang, Daqing, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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94. Edge Coloring Models as Singular Vertex Coloring Models

Author

Szegedy, Balázs, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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95. Regularity Lemmas for Graphs

Author

Rödl, Vojtěch, Schacht, Mathias, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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96. Extremal Graphs and Multigraphs with Two Weighted Colours

Author

Marchant, Edward, Thomason, Andrew, Tóth, Gábor Fejes, editor, Katona, Gyula O. H., editor, Lovász, László, editor, Pálfy, Péter Pál, editor, Recski, András, editor, Stipsicz, András, editor, Szász, Domokos, editor, Miklós, Dezső, editor, Schrijver, Alexander, editor, Szőnyi, Tamás, editor, and Sági, Gábor, editor

Published
2010
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