The vertex set of a 1-interval hypergraph is the set of real numbers; each edge in such a hypergraph is an interval of the real line.
Note the difference from an interval graph: in an interval graph, the vertices are the intervals (a finite set); in a 1-interval hypergraph, the vertices are all points in the real line (an uncountable set).
This is analogous to Kőnig's theorem for bipartite graphs.
Kaiser[2] proved that, in a d-interval hypergraph, τ(H) ≤ d(d – 1)ν(H), and moreover, every d-interval hypergraph with a matching of size m, can be covered by at d(d − 1)m points, (d − 1)m points on each line.
Frick and Zerbib[3] proved a colorful ("rainbow") version of this theorem.