On the extremal solutions for capacitated network problems

In this note we give a unifying approach to the problem of characterizing the extreme points of those convex matrix sets which correspond to the domains of various types of capacitated network problems. It is shown that we can determine whether a matrix is an extreme point of the sets by examining the pattern of a certain graph associated with it. We also study the extreme points of the convex matrix sets which are related to network problems free from capacity constraints by linking them up with certain capacitated network problem.