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Facets of the (s, t)-p-path polytope

机译:(s,t)-p路径多态性的方面

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We give a partial description of the (s, t)-p-path polytope of a directed graph D which isthe convex hull of the incidence vectors of simple directed (s, t)-paths in D of length p.First, we point out how the (s, t)-p-path polytope is located in the family of path and cyclepolyhedra. Next, we give some classes of valid inequalities which are very similar to theinequalities which are valid for the p-cycle polytope, that is, the convex hull of the incidencevectors of simple cycles of length p in D. We give necessary and sufficient conditions forthese inequalities to be facet defining. Furthermore, we consider a class of inequalities thathas been identified to be valid for (s, t)-paths of cardinality at most p. Finally, we transferthe results to related polytopes, in particular, the undirected counterpart of the (s, t)-p-path polytope.
机译:我们给出了有向图D的(s,t)-p路径多边形的部分描述,该图是长度为p的D中简单有向(s,t)路径的入射向量的凸包。找出(s,t)-p路径多态性在路径和循环多面体家族中的位置。接下来,我们给出一些有效不等式,这些有效不等式与对于p循环多态性有效的不等式非常相似,也就是D中长度为p的简单循环的入射向量的凸包。我们给出了必要的充分条件不平等的定义。此外,我们考虑一类不等式,这些不等式已被确定对于最多为p的基数的(s,t)路径有效。最后,我们将结果转移到相关的多表位,特别是(s,t)-p路径多表位的无向对应物。

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