Abstract
Strang (Mathematical Programming 26, 1983) gave a method to establish a max-flow min-cut theorem in a domain of a Euclidean space. The method can be applied also to max-flow min-cut problems defined by Iri (Survey of Mathematical Programming, North-Holland, 1979) whenever the capacity functions of max-flow problems are bounded and continuous. This paper deals with max-flow min-cut problems of Strang and Iri with unbounded or noncontinuous capacity functions. It is proved that, in such problems, max-flow min-cut theorems may fail to hold.
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Nozawa, R. Examples of max-flow and min-cut problems with duality gaps in continuous networks. Mathematical Programming 63, 213–234 (1994). https://doi.org/10.1007/BF01582067
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DOI: https://doi.org/10.1007/BF01582067