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Mat. Sb., 2010, Volume 201, Number 4, Pages 137–160 (Mi msb7480)  

This article is cited in 5 scientific papers (total in 5 papers)

The existence of panchromatic colourings for uniform hypergraphs

D. A. Shabanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The well-known extremal problem concerning panchromatic colouring of hypergraphs is investigated. An $r$-colouring of the set of vertices of a hypergraph is said to be panchromatic if each link of the hypergraph is incident to vertices of all colours. The quantity $p(n,r)$ defined as the minimum number of links in an $n$-uniform hypergraph which admits no panchromatic $r$-colourings is studied. New lower and upper bounds for $p(n,r)$ are obtained, which improve earlier results for many of the relations between the parameters $n$ and $r$. In addition, a sufficient condition for the existence of a panchromatic $r$-colouring of an $n$-uniform hypergraph is obtained.
Bibliography: 18 items.

Keywords: hypergraph, panchromatic colouring, the method of random colouring.

DOI: https://doi.org/10.4213/sm7480

Full text: PDF file (580 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:4, 607–630

Bibliographic databases:

UDC: 519.112.7+519.179.1
MSC: Primary 05C15; Secondary 05C65
Received: 05.11.2008

Citation: D. A. Shabanov, “The existence of panchromatic colourings for uniform hypergraphs”, Mat. Sb., 201:4 (2010), 137–160; Sb. Math., 201:4 (2010), 607–630

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  • https://doi.org/10.4213/sm7480
  • http://mi.mathnet.ru/eng/msb/v201/i4/p137

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shabanov D.A., “On a generalization of Rubin's theorem”, J. Graph Theory, 67:3 (2011), 226–234  crossref  mathscinet  zmath  isi  elib
    2. A. P. Rozovskaya, D. A. Shabanov, “Improvement of the Lower Bound in the Kostochka Problem of Panchromatic Coloring of a Hypergraph”, Math. Notes, 89:6 (2011), 903–906  mathnet  crossref  crossref  mathscinet  isi
    3. A. M. Raigorodskii, D. A. Shabanov, “The Erdős–Hajnal problem of hypergraph colouring, its generalizations, and related problems”, Russian Math. Surveys, 66:5 (2011), 933–1002  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. P. Rozovskaya, D. A. Shabanov, “Extremal problems for panchromatic colourings of uniform hypergraphs”, Discrete Math. Appl., 22:2 (2012), 185–206  mathnet  crossref  crossref  mathscinet  elib  elib
    5. Kang R.J., “Improper Choosability and Property B”, J. Graph Theory, 73:3 (2013), 342–353  crossref  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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