Color-detectors of hypergraphs

Let X be a set of cardinality k, F be a family of subsets of X. We say that a cardinal λ,λ<k, is a color-detector of the hypergraph H=(X,F) if card χ(X)≤λ for every coloring χ:X→k such that card χ(F)≤λ for every F∈F. We show that the color-detectors of H are tightly connected with the coverin...

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Published in:Algebra and Discrete Mathematics
Date:2005
Main Authors: Protasov, I.V., Protasova, O.I.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2005
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/156597
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Color-detectors of hypergraphs / I.V. Protasov, O.I. Protasova // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 84–91. — Бібліогр.: 3 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-156597
record_format dspace
spelling Protasov, I.V.
Protasova, O.I.
2019-06-18T17:33:49Z
2019-06-18T17:33:49Z
2005
Color-detectors of hypergraphs / I.V. Protasov, O.I. Protasova // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 84–91. — Бібліогр.: 3 назв. — англ.
1726-3255
2000 Mathematics Subject Classification: 05C15.
https://nasplib.isofts.kiev.ua/handle/123456789/156597
Let X be a set of cardinality k, F be a family of subsets of X. We say that a cardinal λ,λ<k, is a color-detector of the hypergraph H=(X,F) if card χ(X)≤λ for every coloring χ:X→k such that card χ(F)≤λ for every F∈F. We show that the color-detectors of H are tightly connected with the covering number cov(H)=sup{α: any α points of X are contained in some F∈F}. In some cases we determine all of the color-detectors of H and their asymptotic counterparts. We put also some open questions.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Color-detectors of hypergraphs
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Color-detectors of hypergraphs
spellingShingle Color-detectors of hypergraphs
Protasov, I.V.
Protasova, O.I.
title_short Color-detectors of hypergraphs
title_full Color-detectors of hypergraphs
title_fullStr Color-detectors of hypergraphs
title_full_unstemmed Color-detectors of hypergraphs
title_sort color-detectors of hypergraphs
author Protasov, I.V.
Protasova, O.I.
author_facet Protasov, I.V.
Protasova, O.I.
publishDate 2005
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description Let X be a set of cardinality k, F be a family of subsets of X. We say that a cardinal λ,λ<k, is a color-detector of the hypergraph H=(X,F) if card χ(X)≤λ for every coloring χ:X→k such that card χ(F)≤λ for every F∈F. We show that the color-detectors of H are tightly connected with the covering number cov(H)=sup{α: any α points of X are contained in some F∈F}. In some cases we determine all of the color-detectors of H and their asymptotic counterparts. We put also some open questions.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/156597
citation_txt Color-detectors of hypergraphs / I.V. Protasov, O.I. Protasova // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 84–91. — Бібліогр.: 3 назв. — англ.
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first_indexed 2025-12-07T18:25:48Z
last_indexed 2025-12-07T18:25:48Z
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