A is a hypergraph obtained from by splitting some or all of its vertices into more than one vertex. Amalgamating a hypergraph can be thought of as taking , partitioning its vertices, then for each element of the partition squashing the vertices to form a single vertex in the amalgamated hypergraph . In this paper, we use Nash-Williams lemma on laminar families to prove a detachment theorem for amalgamated 3-uniform hypergraphs, which yields a substantial generalization of previous amalgamation theorems by Hilton, Rodger, and Nash-Williams.
To demonstrate the power of our detachment theorem, we show that the complete 3-uniform n-partite multihypergraph can be expressed as the union of k edge-disjoint factors, where for , is -regular, if and only if:
- for all ,
- for each i, , and