Color-detectors of hypergraphs
Let \(X\) be a set of cardinality \(k\), \(\mathcal{F}\) be a family of subsets of \(X\). We say that a cardinal \(\lambda, \lambda< k\), is a color-detector of the hypergraph \(H=(X, \mathcal{F})\) if card \(\chi(X)\leq \lambda\) for every coloring \(\chi: X\rightarrow k\) such that card ...
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/918 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-9182018-03-21T07:18:38Z Color-detectors of hypergraphs Protasov, I. V. Protasova, O. I. hypergraph, color-detector, covering number 05C15 Let \(X\) be a set of cardinality \(k\), \(\mathcal{F}\) be a family of subsets of \(X\). We say that a cardinal \(\lambda, \lambda< k\), is a color-detector of the hypergraph \(H=(X, \mathcal{F})\) if card \(\chi(X)\leq \lambda\) for every coloring \(\chi: X\rightarrow k\) such that card \(\chi(F)\leq \lambda\) for every \(F\in \mathcal{F}\). We show that the color-detectors of \(H\) are tightly connected with the covering number \(cov (H)=\sup \{\alpha: \text{ any } \alpha \text{ points of } X \text{ are contained in some }\ F\in \mathcal{F} \}\). In some cases we determine all of the color-detectors of \(H\) and their asymptotic counterparts. We put also some open questions. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/918 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/918/447 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T07:18:38Z |
| collection |
OJS |
| language |
English |
| topic |
hypergraph color-detector covering number 05C15 |
| spellingShingle |
hypergraph color-detector covering number 05C15 Protasov, I. V. Protasova, O. I. Color-detectors of hypergraphs |
| topic_facet |
hypergraph color-detector covering number 05C15 |
| format |
Article |
| author |
Protasov, I. V. Protasova, O. I. |
| 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 |
| description |
Let \(X\) be a set of cardinality \(k\), \(\mathcal{F}\) be a family of subsets of \(X\). We say that a cardinal \(\lambda, \lambda< k\), is a color-detector of the hypergraph \(H=(X, \mathcal{F})\) if card \(\chi(X)\leq \lambda\) for every coloring \(\chi: X\rightarrow k\) such that card \(\chi(F)\leq \lambda\) for every \(F\in \mathcal{F}\). We show that the color-detectors of \(H\) are tightly connected with the covering number \(cov (H)=\sup \{\alpha: \text{ any } \alpha \text{ points of } X \text{ are contained in some }\ F\in \mathcal{F} \}\). In some cases we determine all of the color-detectors of \(H\) and their asymptotic counterparts. We put also some open questions. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/918 |
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AT protasoviv colordetectorsofhypergraphs AT protasovaoi colordetectorsofhypergraphs |
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2025-12-02T15:37:36Z |
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2025-12-02T15:37:36Z |
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1850411431119290368 |