It is easy to see that symmetric difference of two matchings are cycles or simple paths. But what about b-matchings? Is there anything known about how they look? Even for restricted cases such as bipartite graphs $G=(U,V,E)$ with $b(v)=1\ \ \forall v\in U $
$def: b-matching$: Given a graph $G=(V,E)$ and an upper bound $b:V\to \mathbb{Z}^+$ for each vertex, a $b-matching$ is a sub-graph $H$ of $G$ such that $deg_H(v) \le b(v) \ \ \forall v\in V$. (Regular matching is a special case when $b(v)=1$)
