Subgraphs of Bipartite and Directed Graphs.

摘要

The main theorem of this memorandum provides necessary and sufficient conditions in order that a locally finite bipartite graph have a subgraph whose valences lie in prescribed intervals. This theorem is applied to the study of integer-valued flows in locally finite directed graphs. In particular, generalizations of the max-flow min-cut theorem and of the circulation theorem are obtained. The axiom of choice is assumed throughout. (Author)