Abstract
The usual linear relaxation of the node-packing problem contains no useful information when the underlying graph G has the property of “bicriticality.” We consider a sparse random graph G n ( m) obtained in the usual way from a random directed graph with fixed out-degree m and show that the probability that G n (2) is bicritical tends to (1−2e −2) 1 2 as n→∞. This confirms a conjecture by G. R. Grimmett and W. R. Pulleyblank ( Oper. Res. Lett., in press).
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