The matchings of a simple graph $G$ form a simplicial complex, which is called the matching complex of $G$. The bounded degree complex is a generalization of matching complexes, and was introduced by Reiner and Roberts.

It is known that the matching complex of a simple graph $G$ is the independence complex of the line graph of $G$. Generalizing this in a natural way, we can regard the bounded degree complex as the independence complex of a certain hypergraph. In this talk, generalizing a method to determine the homotopy types of independence complexes of simple graphs, we show that the bounded degree complex of $G$ has a wedge decomposition when $G$ has a leaf. This result implies the following result which was recently shown by Singh: Every bounded degree complex of a forest is empty or homotopy equivalent to a wedge of spheres.