Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of GLn-Complexes

We present a technique for lifting results on the homology of matching complexes of certain types of graphs and hypergraphs to general bounded degree graph complexes. This technique is based on our observation that homological results of Bouc on matching complexes, of Reiner and Roberts on bounded degree graph complexes, and of Józefiak and Weyman on Koszul complexes are all equivalent.