In this note, we study two rewrite rules on hypergraphs, called edge-domination and node-domination, and show that they are confluent. These rules are rather natural and commonly used before computing the minimum hitting sets of a hypergraph. Intuitively, edge-domination allows us to remove hyperedges that are supersets of another hyperedge, and node-domination allows us to remove nodes whose incident hyperedges are a subset of that of another node. We show that these rules are confluent up to isomorphism, i.e., if we apply any sequences of edge-domination and node-domination rules, then the resulting hypergraphs can be made isomorphic via more rule applications. This in particular implies the existence of a unique minimal hypergraph, up to isomorphism.

翻译：本文研究了超图上的两种重写规则——边支配与节点支配，并证明它们具有合流性。这些规则相当自然，且在计算超图最小命中集之前常被使用。直观而言，边支配允许我们移除作为另一超边超集的超边，而节点支配允许我们移除其关联超边为另一节点关联超边子集的节点。我们证明这些规则在同构意义下具有合流性，即若应用任意序列的边支配与节点支配规则，则所得超图可通过进一步应用规则变为同构。这尤其意味着在同构意义下存在唯一的极小超图。