Book

Dániel Gerbner, Balázs Patkós, Extremal Finite Set Theory, Chapman and Hall/CRC, 2018, 336 pages

Balazs Patkos's Papers

2005 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024
Preprints
Manuscripts

TOP
2005

  • B. Patkos,
    • How different can two intersecting families be,
    Electronic Journal of Combinatorics 12 (2005) R24  

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    2008

  • D. Gerbner, B. Patkos,
    • l-chain profile vectors,
    SIAM Journal on Discrete Mathematics 22 (2008) 1, 185-193.  

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    2009

  • B. Patkos,
    • The distance of F-free families,
    Studia Sci. Math. Hungarica 46 (2009) 2, 275-286.  
  • D. Gerbner, B. Patkos,
    • Profile vectors in the lattice of subspaces,
    Discrete Mathematics, 309 (2009) 2861-2869.  
  • M. Krivelevich, B. Patkos,
    • Equitable coloring of random graphs,
    Random Structures and Algorithms 35 (2009) 83-99.  
  • B. Patkos,
    • $l$-trace $k$-Spener families,
    J. of Combinatorial Theory, Ser. A, 116 (2009) 1047--1055.  
  • B. Patkos, K. Tichler, G. Wiener
    • Inclusionwise minimal completely separating systems,
    Journal of Statistical Theory and Practice, 3 (2009) 459--466.  
  • B. Patkos,
    • Traces of uniform set families,
    Electronic Journal of Combinatorics, 16 (2009) N8  

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    2010

  • D. Gerbner, D. Palvolgyi, B. Patkos, G. Wiener,
    • Selecting the largest and the smallest elements with a lie,
    Discrete Applied Mathematics 158, (2010), 988-995.  
  • D. Gerbner, B. Keszegh, N. Lemons, C. Palmer, D. Palvolgyi, B. Patkos,
    • Polychromatic Colorings of Arbitrary Rectangular Partitions,
    Discrete Mathematics 310 (2010), 21--30.  
  • A. Blokhuis, A.E. Brouwer, A. Chowdhury, P. Frankl, T. Mussche, B. Patkos, T. Szonyi
    • Hilton-Milner theorem for vector spaces,
    Electronic Journal of Combinatorics, 17 (2010), R71  
  • A. Chowdhury, B. Patkos,
    • Shadows and Intersections in Vector Spaces,
    J. of Combinatorial Theory, Ser. A 117 (2010) 1095--1106  
  • B. Patkos,
    • On randomly generated non-trivially intersecting hypergraphs,
    Electronic Journal of Combinatorics (17) (2010), R26  

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    2011

  • P. Balister, B. Patkos,
    • Random partial orders defined by angular domains,
    Order, 28 (2011) 341--355  

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    2012

  • J. Barat, Z. Furedi, I. Kantor, Y. Kim, B. Patkos,
    • Large $B_d$-free and union-free subfamilies,
    SIAM J. on Discrete Mathematics 26 (2012) 71-76  
  • P.L. Erdos, D. Gerbner, N. Lemons, D. Mubayi, C. Palmer, B. Patkos,
    • Two-part set systems,
    Electronic Journal of Combinatorics, 19 (2012), P52  
  • D. Gerbner, N. Lemons, C. Palmer, B. Patkos, V. Szecsi,
    • Cross-Sperner families,
    Studia Sci. Math. Hungarica, 49 (2012), 44-51.  
  • B. Patkos,
    • A note on traces of set families,
    Moscow Journal of Combinatorics and Number Theory, 2 (2012), 47-55.  
  • D. Gerbner, N. Lemons, C. Palmer, B. Patkos, V. Szecsi
    • Almost intersecting families,
    SIDMA, 26 (2012), 1657-1669.  

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    2013

  • Z.L. Nagy, L. Ozkahya, B. Patkos, M. Vizer
    • On the ratio of maximum and minimum degree in maximal intersecting families,
    Discrete Mathematics, 313 (2013), 207-211.  
  • B. Patkos,
    • Families that remain k-Sperner even after omitting an element of their ground set,
    Electronic Journal of Combinatorics, 20 (2013), P32  
  • D. Gerbner, G.O.H. Katona, D. Palvolgyi, B. Patkos
    • On majority and plurality problems , slides
    Discrete Applied Mathematics, 161 (2013), 813-818.  
  • I. Kantor, B. Patkos,
    • Towards a de Bruijn-Erdos theorem in the L_1-metric,
    Discrete and Computational Geometry, 49 (2013), 659-670.  
  • D. Gerbner, N. Lemons, C. Palmer, D. Palvolgyi, B. Patkos, V. Szecsi,
    • Almost Cross-Intersecting and Almost Cross-Sperner Pairs of Families of Sets,
    Graphs and Combinatorics, 29 (2013), 489-498.  
  • D. Gerbner, B. Keszegh, N. Lemons, C. Palmer, D. Palvolgyi, B. Patkos,
    • Saturating Sperner families,
    Graphs and Combinatorics, 29 (2013), 1355-1364.  

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    2014

  • B. Patkos, M. Vizer
    • Game saturation of intersecting families,
    Cent. Eur. J. Math., 2014, 12(9), 1382-1389
  • B. Keszegh, B. Patkos, X. Zhu
    • Nonrepetitive colorings of lexicographic product of paths and other graphs,
    DMTCS, 2014, 16(2), 97-110  

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    2015

  • B. Patkós
    • Induced and non-induced forbidden subposet problems,
    Electronic Journal of Combinatorics, 2015, P1.30
  • A. Grzesik, M. Mikalacki, Z.L. Nagy, A. Naor, B. Patkós, F. Skerman,
    • Avoider-Enforcer star games,
    DMTCS, DMTCS,
  • Z.L. Nagy, B. Patkós
    • On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method ,Electronic Journal of Combinatorics, 2015, P1.83
  • T. Héger, B. Patkós, M. Takáts
    • Search Problems in Vector Spaces,
    Designs, Codes and Criptography, 76 (2) 2015, 207-216
  • Y. Kim, M. Kumbhat, Z.L. Nagy, B. Patkós, A. Pokrovskiy, M. Vizer
    • Identifying codes and searching with balls in graphs,
    Discrete Applied Mathematics, 193, 2015, 39-47
  • B. Patkós
    • Supersaturation and stability for forbidden subposet problems,
    Journal of Combinatorial Theory A, 136, 2015, 220-237.

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    2016

  • B. Bresar, Cs. Bujtás, T. Gologranc, S. Klavzar, G. Kosmrlj, B. Patkós, Zs. Tuza, M. Vizer
    • Dominating sequences in grid-like and toroidal graphs,
    Electronic Journal of Combinatorics, 23 (4) 2016, P4.34

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    2017

  • D. Gerbner, B. Keszegh, D. Pálvölgyi, B. Patkós, M. Vizer, G. Wiener
    • Finding a non-minority ball with majority answers,
    Discrete Applied Mathematics, 219 (2017), 18-31
  • Cs. Bujtás, B. Patkós, Zs. Tuza, M. Vizer
    • The minimum number of vertices in uniform hypergraphs with given domination number,
    Discrete Mathematics, 340:(11) pp. 2704-2713. (2017)
  • Boštjan Brešar, Csilla Bujtás, Tanja Gologranc, Sandi Klavžar, Gašper Košmrlj, Balázs Patkós, Zsolt Tuza, Máté Vizer
  • Grundy dominating sequences and zero forcing sets,
    Discrete Optimization 26: pp. 66-77. (2017)

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    2018

  • Dániel Gerbner, Balázs Keszegh, Cory Palmer, Balázs Patkós
    • On the number of cycles in a graph with restricted cycle lengths,
    SIAM Journal on Discrete Mathematics 2018, Vol. 32, No. 1, pp. 266-279
  • Dániel Gerbner, Balázs Keszegh, Gábor Mészáros, Balázs Patkós, Máté Vizer

    • Line Percolation in Finite Projective Planes
    SIAM Journal on Discrete Mathematics, 32(2), pp.864-881.
  • Dániel Gerbner, Balázs Patkós, Máté Vizer
    • Forbidden subposet problems for traces of set families,
    Electronic Journal of Combinatorics, 25(3) P3.49

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    2019

  • Dániel Gerbner, Balázs Keszegh, Abhishek Methuku, Balázs Patkós, Máté Vizer
    An improvement on the maximum number of k-Dominating Independent Sets,
    Journal of Graph Theory, 91 (1) 88-97
  • Cs. Bujtás, B. Patkós, Zs. Tuza, M. Vizer
    Domination game on uniform hypergraphs,
    Discrete Applied Mathematics, Volume 258, 15 April 2019, Pages 65-75
  • Dániel Gerbner, Abhishek Methuku, Dániel T. Nagy, Balázs Patkós, Máté Vizer
    Stability results on vertex Turán problems in Kneser graphs
    Electronic Journal of Combinatorics, 26 (2) 2019, P2.13
  • Boštjan Brešar, Csilla Bujtás, Tanja Gologranc, Sandi Klavžar, Gašper Košmrlj, Tilen Marc, Balázs Patkós, Zsolt Tuza, Máté Vizer
    The variety of domination games
    Aequationes Mathematicae, 93(6) 2019, 1085-1109
  • Dániel Gerbner, Abhishek Methuku, Dániel T. Nagy, Balázs Patkós, Máté Vizer
    On the number of containments in P-free families
    Graphs and Combinatorics, 35 (6) 2019, 1519-1540
  • Dániel Gerbner, Abhishek Methuku, Dániel T. Nagy, Balázs Patkós, Máté Vizer
    Forbidding rank-preserving copies of a poset,
    Order, 36 (3) 2019, 611-620

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    2020

  • András Gyárfás, Dömötör Pálvölgyi, Balázs Patkós, Matthew Wales
    Distribution of colors in Gallai colorings
    European Journal of Combinatorics, 86, 103087
  • Balázs Patkós
    On colorings of the Boolean lattice avoiding a rainbow copy of a poset
    Discrete Applied Mathematics, 276 (2020), 108-114
  • Dániel Gerbner, Balázs Keszegh, Abhishek Methuku, Dániel T. Nagy, Balázs Patkós, Casey Tompkins, Chuanqi Xiao
    Set systems related to a house allocation problem
    Discrete Mathematics, 343 (7) (2020), 111886
  • Huilan Chang, Dániel Gerbner, Balázs Patkós
    Finding non-minority balls with majority and plurality queries
    Discrete Applied Mathematics, 284 (2020), 631-639.
  • Dániel Gerbner, Balázs Keszegh, Balázs Patkós
    Generalized forbidden subposet problems,
    Order, 37 (2020), 389-410.
  • Dániel Gerbner, Dániel T. Nagy, Balázs Patkós, Máté Vizer
    t-wise Berge and t-heavy hypergraphs
    SIDMA, 34(3) (2020), 1813–1829
  • Balázs Patkós
    On the general position problem on Kneser graphs
    Acta Mathematica Contemporanea, 18 (2) 2020, 273-280

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    2021

  • Gábor Damásdi, Dániel Gerbner, Gyula O. H. Katona, Balázs Keszegh, Dániel Lenger, Abhishek Methuku, Dániel T. Nagy, Dömötör Pálvölgyi, Balázs Patkós, Máté Vizer, Gábor Wiener
    Adaptive Majority Problems for Restricted Query Graphs and for Weighted Sets
    Discrete Applied Mathematics, 288, 2021, 235-245
  • Boštjan Brešar, Csilla Bujtás, Tanja Gologranc, Sandi Klavžar, Gašper Košmrlj, Tilen Marc, Balázs Patkós, Zsolt Tuza, Máté Vizer
    On Grundy total domination number in product graphs
    Discussiones Mathematicae Graph Theory, 41 (1) (2021), 225-248.
  • Dániel Gerbner, Dániel T. Nagy, Balázs Patkós, Máté Vizer
    On the maximum number of copies of H in graphs with given size and order
    Journal of Graph Theory, 96 (1) (2021), 34-43.
  • Dániel Gerbner, Dániel Nagy, Balázs Patkós, Máté Vizer
    Supersaturation, counting, and randomness in forbidden subposet problems
    the Electronic Journal of Combinatorics, 28 (1) 2021 P1.40
  • Dániel Nagy, Balázs Patkós
    On L-close Sperner systems
    Graphs and Combinatorics, 37(3) 789-796
  • Sandi Klavžar, Balázs Patkós, Gregor Rus, Ismael G. Yero
    On general position sets in Cartesian grids
    Results in Mathematics 76, 123 (2021).
  • Balázs Keszegh, Nathan Lemons, Ryan R. Martin, Dömötör Pálvölgyi, Balázs Patkós
    Induced and non-induced poset saturation problems, webinar talk: slides, file, youtube
    Journal of Combinatorial Theory, Series A 184 (2021) 105497
  • Dániel Gerbner, Abhishek Methuku, Dániel T. Nagy, Balázs Patkós, Máté Vizer
    Vertex Turán problems for the oriented hypercube
    Acta Univ. Sapientiae Math., 13 (2021):2 356-366.

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    2022

  • Dániel Gerbner, Balázs Patkós, Zsolt Tuza, Máté Vizer
    On saturation of Berge hypergraphs
    European Journal of Combinatorics 102:103477
  • Dániel Gerbner, Dániel Nagy, Balázs Patkós, Máté Vizer
    Forbidden subposet problems in the grid
    Discrete Mathematics, Volume 345, Issue 3, March 2022, 112720
  • Nóra Frankl, Sergei Kiselev, Andrey Kupavskii, Balázs Patkós
    VC-saturated set systems
    European Journal of Combinatorics, Volume 104, August 2022, 103528
  • Dániel Gerbner, Balázs Patkós, Zsolt Tuza, Máté Vizer
    Saturation problems with regularity constraints
    Discrete Mathematics, Volume 345, Issue 8, August 2022, 112921
  • József Balogh, Ryan R. Martin, Dániel T. Nagy, Balázs Patkós
    On generalized Turán results in height two posets
    SIAM Journal on Discrete Mathematics 36(2):1483-1495
  • Dániel Gerbner, Balázs Patkós, Zsolt Tuza, Máté Vizer
    Singular Turán numbers and WORM-colorings
    Discussiones Mathematicae Graph Theory, 42 (4) (2022) 1061-1074
  • Dániel T. Nagy, Balázs Patkós
    Triangles in intersecting families
    Mathematika, 68 (4) (2022) 1073-1079
  • Dániel Gerbner, Balázs Patkós
    Generalized Turán problems for complete bipartite graphs
    Graphs and Combinatorics, (2022) 38:164
  • Fei-Huang Chang, Dániel Gerbner, Wei-Tian Li, Abhishek Methuku, Dániel Nagy, Balázs Patkós, Máté Vizer
    Rainbow Ramsey problems for the Boolean lattice
    Order, 39 (3) (2022), 453-463.

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    2023

  • Balázs Patkós, Zsolt Tuza, Máté Vizer
    Vector sum-intersection theorems
    Discrete Mathematics, 346 (10) 2023, 113506
  • Cory Palmer, Balázs Patkós
    On the number of maximal independent sets: From Moon-Moser to Hujter-Tuza
    Journal of Graph Theory 104 (2) 2023, 440-445
  • Dániel Gerbner, Balázs Keszegh, Dániel Lenger, Dániel T. Nagy, Dömötör Pálvölgyi, Balázs Patkós, Máté Vizer, Gábor Wiener
    On graphs that contain exactly k copies of a subgraph, and a related problem in search theory
    Discrete Applied Mathematics, 341 2023, 196-203.
  • József Balog, William Linz, Balázs Patkós
    On the sizes of t-intersecting k-chain-free families
    Combinatorial Theory 3 (2) (2023) #13

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    2024

  • Dániel Gerbner, Balázs Patkós
    Generalized Turán results for intersecting cliques
    Discrete Mathematics, Volume 347, Issue 1, January 2024, 113710
  • Dániel Gerbner, Balázs Patkós, Zsolt Tuza, Máté Vizer
    Some exact results for regular Turán problems for all large orders
    European Journal of Combinatorics, 117 (2024) 103828
  • Balázs Patkós, Andrew Treglown
    On some extremal and probabilistic questions for tree posets
    Electronic Journal of Combinatorics, 31 (1) (2024) P1.19
  • Dániel Gerbner, Dániel Nagy, Balázs Patkós, Nika Salia, Máté Vizer
    Stability of extremal connected hypergraphs avoiding Berge-paths, slides
    European Journal of Combinatorics, 118 (2024) 103930
  • Balázs Patkós, Zsolt Tuza, Máté Vizer
    Extremal graph theoretic questions for q-ary vectors
    Graphs and Combinatorics, 40 (2024) 57
  • Balázs Patkós, Milos Stojakovic, Máté Vizer
    The Constructor-Blocker game
    Applicable Analysis and Discrete Mathematics, 18 (2024), 193–214
  • Yair Caro, Balázs Patkós, Zsolt Tuza, Máté Vizer
    Counting Connected Partitions of Graphs
    Journal of Graph Theory, 107 2 (2024), 381-392
  • Gábor Bacsó, Balázs Patkós, Zsolt Tuza, Máté Vizer
    The robust chromatic number of graphs
    Graphs and Combinatorics 40, 89 (2024).
  • Yair Caro, Balázs Patkós, Zsolt Tuza
    Connected Turán number of trees
    Ars Mathematica Contemporeana, 24 (4) 2024, P4.01
  • Dániel Gerbner, Balázs Keszegh, Dániel T. Nagy, Kartal Nagy, Dömötör Pálvölgyi, Balázs Patkós, Gábor Wiener
    <Query complexity of Boolean functions on the middle slice of the cube
    Discrete Applied Mathematics, 362 (2024) 43-49.

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    Preprints

  • Dániel Gerbner, Balázs Keszegh, Kartal Nagy, Balázs Patkós, Gábor Wiener
    Cooperation in Combinatorial Search
    accepted to Optimization Letters
  • Gábor Bacsó, Csilla Bujtás, Balázs Patkós, Zsolt Tuza, Máté Vizer
    The robust chromatic number of certain graph classes
    submitted
  • Dömötör Pálvölgyi, Balázs Patkós
    Projective and external saturation problem for posets
    to appear in Order
  • Yair Caro, Balázs Patkós, Zsolt Tuza, Máté Vizer
    Edge mappings of graphs: Ramsey type parameters
    submitted
  • Yair Caro, Balázs Patkós, Zsolt Tuza, Máté Vizer
    Edge mappings of graphs: Turán type parameters
    submitted
  • Dániel Gerbner, Balázs Patkós
    A note on vertex Turán problems in the Kneser cube
    submitted
  • Balázs Patkós, Milos Stojakovic, Jelena Stratijev, Máté Vizer
    Generalized saturation game
    submitted
  • Ryan R. Martin, Balázs Patkós
    A note on the Erdos Matching Conjecture
    accepted to Studia Scientiarum Mathematicarum Hungarica: Combinatorics, Geometry and Topology
  • Ryan R. Martin, Balázs Patkós
    On a generalization of a result of Kleitman
    submitted

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    Manuscripts

  • B. Patkos,
    • On tight paths of fixed ength,
     
  • P. Balister, B. Bollobas, B. Patkos,
    • Continuum percolations with steps in line segments,
     
  • B. Patkos,
    • AZ-type identities,