Color-detectors of hypergraphs

• Date: 2018
• Main Authors: Protasov, I. V., Protasova, O. I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: hypergraph; color-detector; covering number; 05C15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/918
• Journal Title: Algebra and Discrete Mathematics

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 ...