Extending Ghouila-Houri's Characterization of Comparability Graphs to Temporal Graphs
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arXiv
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| Format: | Preprint |
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2025
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| author | Charbit, Pierre Habib, Michel Sorondo, Amalia |
| author_facet | Charbit, Pierre Habib, Michel Sorondo, Amalia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Ghouila-Houri's Characterization of Comparability Graphs to Temporal Graphs Charbit, Pierre Habib, Michel Sorondo, Amalia Combinatorics Discrete Mathematics Data Structures and Algorithms 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. |
| title | Extending Ghouila-Houri's Characterization of Comparability Graphs to Temporal Graphs |
| topic | Combinatorics Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.06849 |