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  1. No Access

    Article

    Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite

    We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known to be finite for structures in a non-binary language.

    Martin Balko, David Chodounský, Jan Hubička, Matěj Konečný, Lluis Vena in Combinatorica (2022)

  2. No Access

    Article

    Hypergraph Based Berge Hypergraphs

    Fix a hypergraph \({\mathcal {F}}\) F . A hypergraph

    Martin Balko, Dániel Gerbner, Dong Yeap Kang, Youn** Kim… in Graphs and Combinatorics (2021)

  3. Article

    Open Access

    Almost-Equidistant Sets

    For a positive integer d, a set of points in d-dimensional Euclidean space is called almost-equidistant if for any three points from the set, some two are at unit distance. Let f(d) denote the largest size of an ...

    Martin Balko, Attila Pór, Manfred Scheucher, Konrad Swanepoel… in Graphs and Combinatorics (2020)

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  4. No Access

    Article

    Covering Lattice Points by Subspaces and Counting Point–Hyperplane Incidences

    Let d and k be integers with \(1 \le k \le d-1\) ...

    Martin Balko, Josef Cibulka, Pavel Valtr in Discrete & Computational Geometry (2019)

  5. No Access

    Article

    Drawing Graphs Using a Small Number of Obstacles

    An obstacle representation of a graph G is a set of points in the plane representing the vertices of G, together with a set of polygonal obstacles such that two vertices of G are connected by an edge in G if and ...

    Martin Balko, Josef Cibulka, Pavel Valtr in Discrete & Computational Geometry (2018)

  6. Article

    Open Access

    On the Beer Index of Convexity and Its Variants

    Let S be a subset of \(\mathbb {R}^d\) ...

    Martin Balko, Vít Jelínek, Pavel Valtr… in Discrete & Computational Geometry (2017)

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  7. No Access

    Article

    Crossing Numbers and Combinatorial Characterization of Monotone Drawings of \(K_n\)

    In 1958, Hill conjectured that the minimum number of crossings in a drawing of \(K_n\) ...

    Martin Balko, Radoslav Fulek, Jan Kynčl in Discrete & Computational Geometry (2015)