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R-separating Sets

Published online by Cambridge University Press:  20 November 2018

R. E. Gomory ,
T. C. Hu  and
J. M. Yohe
R. E. Gomory
Affiliation:
IBM Research Center; University of Wisconsin, Madison, Wisconsin
T. C. Hu
Affiliation:
IBM Research Center; University of Wisconsin, Madison, Wisconsin
J. M. Yohe
Affiliation:
IBM Research Center; University of Wisconsin, Madison, Wisconsin
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This study of r-separating sets was originally motivated by the maximum-flow-minimum-cut theorem of finite networks [1 ; 2]. In working toward a continuous version of the maximum-flow-minimum-cut theorem from the usual discrete version, one is led directly to the notion of r-connectedness of a set as defined below. This notion of r-connectedness also has a very simple intuitive interpretation. Intuitively speaking, a set of points in the plane is r-connected if a person starting at any one point of the set is able to reach any other point of the set by jumping from point to point within the set, but never jumping a distance exceeding r in any one jump.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1418 - 1429
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Ford, L. R., Jr., and Fulkerson, P. R., Maximal flow through a network, Can. J. Math. 8 (1956), 399–404.Google Scholar
2. Hu, T. C., Integer programming and network flows (Addison-Wesley, Reading, Mass., 1969), pp. 214–224.Google Scholar
3. Newman, M. H. A., Elements of the topology of plane sets of points (Cambridge University Press, New York, 1961).Google Scholar