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Given a graph $G=(V,E)$ and a set of integers $B(v)$ associated to each vertex, a general factor of $G$ is a set of edges $F\subseteq E$ such that the degree of each vertex $v\in V$ in the graph $(V, ...

Aharoni, Nash-Williams, and Shelah have extended the famous marriage theorem for finite bipartite graphs due to Hall to arbitrary graphs. Is there a similar generalization of Tutte's theorem on ...