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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 5(401), Pages 109–182 (Mi umn9443)  

This article is cited in 19 scientific papers (total in 19 papers)

The Erdős–Hajnal problem of hypergraph colouring, its generalizations, and related problems

A. M. Raigorodskiiab, D. A. Shabanovab

a M. V. Lomonosov Moscow State University
b Moscow Institute of Physics and Technology

Abstract: Extremal problems concerned with hypergraph colouring first arose in connection with classical investigations in the 1920-30s which gave rise to Ramsey theory. Since then, this area has assumed a central position in extremal combinatorics. This survey is devoted to one well-known problem of hypergraph colouring, the Erdős–Hajnal problem, initially posed in 1961. It opened a line of research in hypergraph theory whose methods and results are widely used in various domains of discrete mathematics.
Bibliography: 109 titles.

Keywords: hypergraph, hypergraph colourings, chromatic numbers, extremal set theory.


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English version:
Russian Mathematical Surveys, 2011, 66:5, 933–1002

Bibliographic databases:

Document Type: Article
UDC: 519.112.7+519.174+519.179.1
MSC: 05C15, 05C35, 05C65
Received: 01.11.2010

Citation: A. M. Raigorodskii, D. A. Shabanov, “The Erdős–Hajnal problem of hypergraph colouring, its generalizations, and related problems”, Uspekhi Mat. Nauk, 66:5(401) (2011), 109–182; Russian Math. Surveys, 66:5 (2011), 933–1002

Citation in format AMSBIB
\by A.~M.~Raigorodskii, D.~A.~Shabanov
\paper The Erd\H os--Hajnal problem of hypergraph colouring, its generalizations, and related problems
\jour Uspekhi Mat. Nauk
\yr 2011
\vol 66
\issue 5(401)
\pages 109--182
\jour Russian Math. Surveys
\yr 2011
\vol 66
\issue 5
\pages 933--1002

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    This publication is cited in the following articles:
    1. Raigorodskii A.M., “Izbrannye zadachi kombinatornoi geometrii i teorii grafov”, Tr. Moskovskogo fiziko-tekhnicheskogo instituta, 3:4 (2011), 127–139  elib
    2. Shabanov D.A., “Ob odnom obobschenii zadachi Erdesha-Lovasa”, Tr. Moskovskogo fiziko-tekhnicheskogo instituta, 4:1(13) (2012), 131–140  elib
    3. Teplyakov S.M., “Rekurrentnye verkhnie otsenki v zadache Erdesha-Khainala o raskraske gipergrafa i v ee obobscheniyakh”, Tr. Moskovskogo fiziko-tekhnicheskogo instituta, 4:1(13) (2012), 141–150  elib
    4. Raigorodskii A.M., “Predislovie redaktora nomera”, Tr. Moskovskogo fiziko-tekhnicheskogo instituta, 4:1(13) (2012), 4–11  elib
    5. S. M. Teplyakov, “Upper Bound in the Erdős–Hajnal Problem of Hypergraph Coloring”, Math. Notes, 93:1 (2013), 191–195  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. D. A. Shabanov, “Van der Waerden function and colorings of hypergraphs with large girth”, Dokl. Math., 88:1 (2013), 473–477  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. I. A. Akolzin, “On the Erdős–Hajnal Problem for $3$-Uniform Hypergraphs”, Math. Notes, 94:6 (2013), 951–953  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. L. I. Bogolyubskii, A. S. Gusev, M. M. Pyaderkin, A. M. Raigorodskii, “Independence numbers and chromatic numbers of random subgraphs in some sequences of graphs”, Dokl. Math., 90:1 (2014), 462–465  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    9. A. V. Lebedeva, “Ob algoritmicheskikh metodakh issledovaniya dvukhtsvetnykh raskrasok gipergrafov”, Fundament. i prikl. matem., 19:2 (2014), 125–149  mathnet  mathscinet; A. V. Lebedeva, “On algorithmic methods of analysis of two-colorings of hypergraphs”, J. Math. Sci., 213:2 (2016), 211–229  crossref
    10. D. A. Shabanov, “A generalization of the Hajnal-Szemerédi theorem for uniform hypergraphs”, Dokl. Math., 90:3 (2014), 671  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    11. D. A. Shabanov, “Around Erdős–Lovász problem on colorings of non-uniform hypergraphs”, Discrete Math., 338:11 (2015), 1976–1981  crossref  mathscinet  zmath  isi  elib  scopus
    12. A. E. Khuzieva, D. A. Shabanov, “On regular hypergraphs with high girth and high chromatic number”, Discrete Math. Appl., 25:5 (2015), 277–294  mathnet  crossref  crossref  mathscinet  isi  elib
    13. A. E. Khuzieva, D. A. Shabanov, “Quantitative Estimates of Characteristics for Hypergraphs of Large Girth and Large Chromatic Number”, Math. Notes, 98:6 (2015), 995–998  mathnet  crossref  crossref  mathscinet  isi  elib
    14. Cherkashin D.D., Kozik J., “a Note on Random Greedy Coloring of Uniform Hypergraphs”, 47, no. 3, 2015, 407–413  crossref  mathscinet  zmath  isi
    15. I. R. Shirgazina, “Equitable Colorings of Nonuniform Hypergraphs”, Math. Notes, 99:3 (2016), 444–456  mathnet  crossref  crossref  mathscinet  isi  elib
    16. Kozik J., “Multipass Greedy Coloring of Simple Uniform Hypergraphs”, 48, no. 1, 2016, 125–146  crossref  mathscinet  zmath  isi
    17. Kozik J., Shabanov D., “Improved Algorithms For Colorings of Simple Hypergraphs and Applications”, 116, 2016, 312–332  crossref  mathscinet  zmath  isi
    18. Yu. A. Demidovich, A. M. Raigorodskii, “2-Colorings of Uniform Hypergraphs”, Math. Notes, 100:4 (2016), 629–632  mathnet  crossref  crossref  mathscinet  isi  elib
    19. Akolzin I., Shabanov D., “Colorings of hypergraphs with large number of colors”, Discret. Math., 339:12 (2016), 3020–3031  crossref  mathscinet  zmath  isi  elib  scopus
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