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Diskr. Mat., 2010, Volume 22, Issue 3, Pages 94–109 (Mi dm1110)  

This article is cited in 2 scientific papers (total in 2 papers)

On proper colourings of hypergraphs using prescribed colours

A. P. Rozovskaya, D. A. Shabanov


Abstract: We consider a generalisation of the classic combinatorial problem of P. Erdős and A. Hajnal in the theory of hypergraphs to the case of prescribed colourings. We investigate the value $m_{pr}(n,r)$ equal to the minimum number of edges of a hypergraph in the class of $n$-uniform hypergraphs with prescribed chromatic number greater than $r$. We obtain a lower bound for this value which is better than the known results for $r\ge3$. Moreover, we give a sufficient conditions for existence of a prescribed $r$-colourability of an $n$-uniform hypergraph in terms of restrictions on the intersections of edges. As a corollary we obtain a new bound for the characteristic $m_{pr}^*(n,r)$ equal to the minimum number of edges of a hypergraph in the class of $n$-uniform simple hypergraphs (in which any two edges have at most one common vertex) with the prescribed chromatic number greater than $r$.

DOI: https://doi.org/10.4213/dm1110

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English version:
Discrete Mathematics and Applications, 2010, 20:4, 391–409

Bibliographic databases:

Document Type: Article
UDC: 519.11
Received: 19.12.2008

Citation: A. P. Rozovskaya, D. A. Shabanov, “On proper colourings of hypergraphs using prescribed colours”, Diskr. Mat., 22:3 (2010), 94–109; Discrete Math. Appl., 20:4 (2010), 391–409

Citation in format AMSBIB
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\by A.~P.~Rozovskaya, D.~A.~Shabanov
\paper On proper colourings of hypergraphs using prescribed colours
\jour Diskr. Mat.
\yr 2010
\vol 22
\issue 3
\pages 94--109
\mathnet{http://mi.mathnet.ru/dm1110}
\crossref{https://doi.org/10.4213/dm1110}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2762805}
\elib{http://elibrary.ru/item.asp?id=20730350}
\transl
\jour Discrete Math. Appl.
\yr 2010
\vol 20
\issue 4
\pages 391--409
\crossref{https://doi.org/10.1515/DMA.2010.024}
\elib{http://elibrary.ru/item.asp?id=22139434}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77958514022}


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  • https://doi.org/10.4213/dm1110
  • http://mi.mathnet.ru/eng/dm/v22/i3/p94

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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. 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
    2. Shabanov D.A., “On $r$-chromatic hypergraphs”, Discrete Math., 312:2 (2012), 441–458  crossref  mathscinet  zmath  isi  elib
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