# Is Isomorphism of bounded degree hyper-graphs in P?

Informally, hypergraph is a generalization of a graph in which an edge can join any number of vertices.

A hyper graph G=(V,E) is a two tuple, where $V$ is the set of vertices and $E$ is a set contain subsets of the vertex set of $V$. An example of hyper-graph is given below and for example edge $e_3$ is a subset contain $v_3,v_5,v_6$ and similarly for other edges.

Isomorphism : Two hyper graphs $G(V,E)$ and $H(V,E')$ are isomorphic if there is a permutation $g$ on $V$ such that, $\forall$ $e \in E$, $$e\in E \iff g(e) \in E'$$

Reference: https://en.wikipedia.org/wiki/Hypergraph

Let me define the degree of a vertex in a hyper-graph:

$$D_v = |\{e_i \mid v\in e_i, e_i \in E\} |$$

Question : Is Isomorphism of bounded degree hyper-graphs in P ?

Unbounded uniformity In this case the problem is GI-complete. Given a graph $G$, create a bounded degree hypergraph whose vertices are the edges of $G$ and whose hyperedges correspond to vertices of $G$; a hyperedge contains a vertex if the corresponding vertex of $G$ belongs to the corresponding edge of $G$. This hypergraph has maximum degree 2. Two graphs are isomorphic if and only if the corresponding hypergraphs are isomorphic (this requires some argument but seems correct).