On the existence of an integral potential in a weighted bidirected graph. (English) Zbl 0726.05050
Summary: A. Schrijver proved that if A denotes the incidence matrix of a bidirected graph, and b is an integral “length” function on the edges of A, then the system Ax\(\leq b\) has an integer solution x if and only if (i) each cycle in A has nonnegative length, and (ii) each doubly odd cycle in A has positive length. Unfortunately these cycles may be very complicated. We show that we may restrict conditions (i) and (ii) to a set of reasonably simple cycles.
References:
| [1] | Korach, E., Packing of \(T\)-cuts, and Other Aspects of Dual Integrality, Ph.D. Thesis (1982), Waterloo, Ontario |
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