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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| Дата: | 2005 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156597 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156597 |
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irk-123456789-1565972019-06-19T01:25:59Z Color-detectors of hypergraphs Protasov, I.V. Protasova, O.I. 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. 2005 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/156597 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Protasov, I.V. Protasova, O.I. |
| spellingShingle |
Protasov, I.V. Protasova, O.I. Color-detectors of hypergraphs Algebra and Discrete Mathematics |
| author_facet |
Protasov, I.V. Protasova, O.I. |
| author_sort |
Protasov, I.V. |
| title |
Color-detectors of hypergraphs |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT protasoviv colordetectorsofhypergraphs AT protasovaoi colordetectorsofhypergraphs |
| first_indexed |
2023-05-20T17:50:06Z |
| last_indexed |
2023-05-20T17:50:06Z |
| _version_ |
1796154193893916672 |