Abstract
A hypergraph H = (V, E) has the property Bk if there exists an assignment of two colors to V such that each edge contains at least k vertices of each color. A hypergraph is called simple if every two edges of it have at most one common vertex. We obtain a new lower bound for the minimal number of edges of n-uniform simple hypergraph without the property Bk.
Originally published in Diskretnaya Matematika (2020) 32, №4, 10–37 (in Russian).
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Funding: The reported study was funded by RFBR, project number 19-31-90016.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Diagnostic tests for discrete functions defined on rings
- New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk
- On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions
- On some limit properties for the power series distribution
- Estimates of lengths of shortest nonzero vectors in some lattices. I
Articles in the same Issue
- Frontmatter
- Diagnostic tests for discrete functions defined on rings
- New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk
- On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions
- On some limit properties for the power series distribution
- Estimates of lengths of shortest nonzero vectors in some lattices. I