We show that, in any undirected graph, splitting off can be performed while preserving all cuts of value at most 4/3 times the minimum value, and this is best possible. This generalizes a classical splitting-off result of Lovasz.

The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost....

In this note we give an alternate proof that a scheduling algorithm of Lawler [3,4] finds the optimal solution for 1 / prec / SIGMAj wj Cj when the precedence constraints are series-parallel. We do this by using a linear programming formulation of 1 / prec / SIGMAj wj Cj introduced by Queyranne...