Series–parallel graphs are known to be precisely the graphs for which the standard linear systems describing the cut cone, the cycle cone, the $T$-join polytope, the cut polytope, the multicut polytope and the $T$-join dominant are TDI. We prove that these systems are actually box-TDI. As a byproduct, our result yields a min–max relation for a new problem: the trader multiflow problem. The latter generalizes both the maximum multiflow and min-cost multiflow problems and we show that it is polynomial-time solvable in series–parallel graphs.

中文翻译：

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串行-平行图表的Trader多流程和箱型TDI系统

众所周知，串联-平行图是精确的图，其中描述切锥，循环锥， $Ť$-连接多义词，切多义词，多切多义词和 $Ť$-join占主导地位的是TDI。我们证明这些系统实际上是盒装TDI。作为副产品，我们的结果产生了一个新问题（交易者多流问题）的最小-最大关系。后者概括了最大多流问题和最小成本多流问题，并且我们证明它在串并联图中是多项式时间可解的。