# What is a hypergraph minor?

Is there a theory of hypergraph minors? I could only find some attempts to define them at papers/theses, whose main topic was something else. What would be a useful definition? Does the hypergraph version of the Robertson–Seymour theorem hold?

• Arguably one of the baby steps of graph minor theory is the Wagner theorem on planar graphs. Already this is highly non-trivial for hypergraphs. Recent work of Carmesin has provided a finite list of forbidden minors (for some definition of minor) for the embeddability of simply-connected locally 3-connected 2-complexes in R^3, but there are infinite antichains when these hypotheses are lifted. Related notions of minor towards embedabillity have also been introduced by Nevo and Wagner – Arnaud Mar 8 at 14:47

Let $$H$$ and $$H′$$ be hypergraphs. Then $$H$$ is a minor of $$H′$$ if $$H$$ can be obtained from $$H′$$ by a sequence of operations of the following kinds:
• addition of ahyperedge $$e$$ such that the set $$e$$ induces a clique in the underlying graph, and