The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper we completely characterize the pairs (graph, matching complex) for which the matching complex is a homology manifold, with or without boundary. Except in dimension two, all of these manifolds are sphere or balls.

中文翻译：

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歧管匹配复合物

图的匹配复数是单纯复数，其顶点集是图的边集，每个独立边集都有一个面。在本文中，我们完整地描述了匹配复合体是同源流形的对（图，匹配复合体），有边界或没有边界。除了在第二维中，所有这些流形都是球体或球体。