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 cov...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156597 |
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| Zitieren: | 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| _version_ | 1862720384562888704 |
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| author | Protasov, I.V. Protasova, O.I. |
| author_facet | Protasov, I.V. Protasova, O.I. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T18:25:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156597 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:25:48Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Color-detectors of hypergraphs Protasov, I.V. Protasova, O.I. |
| title | Color-detectors of hypergraphs |
| title_full | Color-detectors of hypergraphs |
| title_fullStr | Color-detectors of hypergraphs |
| title_full_unstemmed | Color-detectors of hypergraphs |
| title_short | Color-detectors of hypergraphs |
| title_sort | color-detectors of hypergraphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156597 |
| work_keys_str_mv | AT protasoviv colordetectorsofhypergraphs AT protasovaoi colordetectorsofhypergraphs |