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 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1726-3255 |