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Network Flow and Systems of Representatives

Published online by Cambridge University Press:  20 November 2018

L. R. Ford Jr.  and
D. R. Fulkerson
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The theory developed for the study of flows in networks (2; 3; 4; 5; 6; 7) sometimes provides a useful tool for dealing with certain kinds of combinatorial problems, as has been previously indicated in (3; 4; 6; 7). In particular, Hall-type theorems for the existence of systems of distinct representatives which contain a prescribed set of marginal elements (10; 11), or, more generally, whose intersection with each member of a given partition of the fundamental set has a cardinality between prescribed lower and upper bounds (9), can be obtained in this way (7).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 78 - 84
Copyright
Copyright © Canadian Mathematical Society 1958

References

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