On the extremal solutions for capacitated network problems. (English) Zbl 0589.05042
The paper gives 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 one can ascertain whether a matrix is an extreme point of the sets by examining the pattern of a certain graph associated with it.
Reviewer: W.-K.Chen
MSC:
| 05C35 | Extremal problems in graph theory |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 94C15 | Applications of graph theory to circuits and networks |
References:
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| [2] | Brualdi R. A., Colloquio Internazionale sulle Teorie Combinatorie (Roma, 1973) pp 99– (1976) |
| [3] | Ford L. R, Flows in Network (1962) |
| [4] | Jurkat W. B., J. Algebra 5 pp 342– (1967) · Zbl 0178.03302 · doi:10.1016/0021-8693(67)90044-0 |
| [5] | Koontz W., J. of Combinatorial Theory (A) 24 pp 111– (1978) · Zbl 0364.15014 · doi:10.1016/0097-3165(78)90049-3 |
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