Abstract
We prove that the minimum number of vertices of a hypergraph that contains every d-uniform hypergraph on k vertices as an induced subhypergraph is (1 + o(1))2 \Bigl(k d \Bigr) /k. The proof relies on the probabilistic method and provides a nonconstructive solution. In addition we exhibit an explicit construction of a hypergraph on \Theta (2 \Bigl(k d \Bigr) /k) vertices, containing every d-uniform hypergraph on k vertices as an induced subhypergraph.
Original language | English |
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Pages (from-to) | 629-642 |
Number of pages | 14 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 33 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Keywords
- Hypergraph
- Labeling
- Universal