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 |
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| Date: | 2005 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| 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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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 |
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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. |
| work_keys_str_mv |
AT protasoviv colordetectorsofhypergraphs AT protasovaoi colordetectorsofhypergraphs |
| first_indexed |
2025-12-07T18:25:48Z |
| last_indexed |
2025-12-07T18:25:48Z |
| _version_ |
1850874998536798208 |