Article ID: | iaor19951845 |
Country: | Netherlands |
Volume: | 63 |
Issue: | 2 |
Start Page Number: | 213 |
End Page Number: | 234 |
Publication Date: | Jan 1994 |
Journal: | Mathematical Programming (Series A) |
Authors: | Nozawa Ryohei |
Keywords: | duality |
Strang 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 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.