A Graph Minors Approach to Temporal Sequences
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912303596699648 |
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| author | Carmesin, Johannes Turner, Will J. |
| author_facet | Carmesin, Johannes Turner, Will J. |
| contents | We develop a structural approach to simultaneous embeddability in temporal sequences of graphs, inspired by graph minor theory. Our main result is a classification theorem for 2-connected temporal sequences: we identify five obstruction classes and show that every 2-connected temporal sequence is either simultaneously embeddable or admits a sequence of improvements leading to an obstruction. This structural insight leads to a polynomial-time algorithm for deciding the simultaneous embeddability of 2-connected temporal sequences.
The restriction to 2-connected sequences is necessary, as the problem is NP-hard for connected graphs, while trivial for 3-connected graphs. As a consequence, our framework also resolves the rooted-tree SEFE problem, a natural extension of the well-studied sunflower SEFE. More broadly, our results demonstrate the applicability of graph minor techniques to evolving graph structures and provide a foundation for future algorithmic and structural investigations in temporal graph theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Graph Minors Approach to Temporal Sequences Carmesin, Johannes Turner, Will J. Combinatorics 05C10, 05C83, 05C75, 57M15, 68R10 We develop a structural approach to simultaneous embeddability in temporal sequences of graphs, inspired by graph minor theory. Our main result is a classification theorem for 2-connected temporal sequences: we identify five obstruction classes and show that every 2-connected temporal sequence is either simultaneously embeddable or admits a sequence of improvements leading to an obstruction. This structural insight leads to a polynomial-time algorithm for deciding the simultaneous embeddability of 2-connected temporal sequences. The restriction to 2-connected sequences is necessary, as the problem is NP-hard for connected graphs, while trivial for 3-connected graphs. As a consequence, our framework also resolves the rooted-tree SEFE problem, a natural extension of the well-studied sunflower SEFE. More broadly, our results demonstrate the applicability of graph minor techniques to evolving graph structures and provide a foundation for future algorithmic and structural investigations in temporal graph theory. |
| title | A Graph Minors Approach to Temporal Sequences |
| topic | Combinatorics 05C10, 05C83, 05C75, 57M15, 68R10 |
| url | https://arxiv.org/abs/2504.00704 |