An orientation of a given static graph is called transitive if for any three vertices $a,b,c$, the presence of arcs $(a,b)$ and $(b,c)$ forces the presence of the arc $(a,c)$. If only the presence of an arc between $a$ and $c$ is required, but its orientation is unconstrained, the orientation is called quasi-transitive. A fundamental result presented by Ghouila-Houri guarantees that any static graph admitting a quasi-transitive orientation also admits a transitive orientation. In a seminal work, Mertzios et al. introduced the notion of temporal transitivity in order to model information flows in simple temporal networks. We revisit the model introduced by Mertzios et al. and propose an analogous to Ghouila-Houri's characterization for the temporal scenario. We present a structure theorem that will allow us to express by a 2-SAT formula all the constraints imposed by temporal transitive orientations. The latter produces an efficient recognition algorithm for graphs admitting such orientations. Additionally, we extend the temporal transitivity model to temporal graphs having multiple time-labels associated to their edges and claim that the previous results hold in the multilabel setting. Finally, we propose a characterization of temporal comparability graphs via forbidden temporal ordered patterns.

翻译：若对于任意三个顶点$a,b,c$，弧$(a,b)$和$(b,c)$的存在强制要求弧$(a,c)$的存在，则给定静态图的一个定向称为传递的。若仅要求$a$与$c$之间存在一条弧，但其方向不受约束，则该定向称为拟传递的。Ghouila-Houri提出的一个基本结果保证，任何允许拟传递定向的静态图也允许传递定向。在一项开创性工作中，Mertzios等人引入了时序传递性的概念，以对简单时序网络中的信息流进行建模。我们重新审视Mertzios等人提出的模型，并针对时序场景提出了一个类似于Ghouila-Houri特征的刻画。我们提出了一个结构定理，该定理将允许我们通过一个2-SAT公式来表达时序传递定向所施加的所有约束。后者产生了一种高效的识别算法，用于判定允许此类定向的图。此外，我们将时序传递性模型扩展到其边关联多个时间标签的时序图，并断言先前结果在多标签设置下仍然成立。最后，我们通过禁止的时序有序模式提出了时序可比图的一个刻画。