Name
Abstract | ||
|---|---|---|
For a hypergraph H=(V,E), a subfamily C⊆E is called a cover of the hypergraph if ⋃C=⋃E. A cover C is called minimal if each cover D⊆C of the hypergraph H coincides with C. We prove that for a hypergraph H the following conditions are equivalent: (i) each countable subhypergraph of H has a minimal cover; (ii) each non-empty subhypergraph of H has a maximal edge; (iii) H contains no isomorphic copy of the hypergraph (ω,ω). This characterization implies that a countable hypergraph (V,E) has a minimal cover if every infinite set I⊆V contains a finite subset F⊆I such that the family of edges EF≔{E∈E:F⊆E} is finite. Also we prove that a hypergraph (V,E) has a minimal cover if sup{|E|:E∈E}<ω or for every v∈V the family Ev≔{E∈E:v∈E} is finite. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.disc.2019.06.014 | Discrete Mathematics |
Keywords | Field | DocType |
Hypergraph,Cover,Minimal cover | Discrete mathematics,Combinatorics,Countable set,Hypergraph,Constraint graph,Infinite set,Isomorphism,Mathematics | Journal |
Volume | Issue | ISSN |
342 | 11 | 0012-365X |
Citations | PageRank | References |
1 | 0.35 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Taras O. Banakh | 1 | 9 | 7.24 |
| Dominic van der Zypen | 2 | 1 | 0.35 |