A perfect matching in a hypergraph is a set of edges that partition the set of vertices. We study the complexity of deciding the existence of a perfect matching in orderable and separable hypergraphs. We show that the class of orderable hypergraphs is strictly contained in the class of separable hypergraphs. Accordingly, we show that for each fixed $k$, deciding perfect matching for orderable $k$-hypergraphs is polynomial time doable, but for each fixed $k\geq 3$, it is NP-complete for separable hypergraphs.

翻译：高光谱中完美的匹配是一组能分割这组脊椎的边缘。 我们研究了在有秩序和可分离的高光谱中决定是否存在完美匹配的复杂程度。 我们显示,有秩序高光谱的类别严格包含在可分离的高光谱类别中。 因此, 我们显示,对于每个固定的 $k$,决定对可排序的 $k$-hyperphraphy 的完美匹配是可操作的, 但是对于每个固定的 $k\geq 3 $, 它对可分离的高光谱来说是完全的。