First-Order Logic and Twin-Width for Some Geometric Graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915694697775104 |
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| author | Geniet, Colin Kim, Gunwoo Meijer, Lucas |
| author_facet | Geniet, Colin Kim, Gunwoo Meijer, Lucas |
| contents | For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence is called delineation, and more generally holds for circle graphs, rooted directed path graphs, and $H$-graphs when $H$ is a forest. Delineation is based on the key idea that geometric graphs often admit natural vertex orderings, allowing to use the very rich theory of twin-width for ordered graphs.
Answering two questions raised in their work, we prove that delineation holds for intersection graphs of non-degenerate axis-parallel unit segment graphs, but fails for visibility graphs of 1.5D terrains. We also prove delineation for intersection graphs of circular arcs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First-Order Logic and Twin-Width for Some Geometric Graphs Geniet, Colin Kim, Gunwoo Meijer, Lucas Discrete Mathematics Logic in Computer Science Combinatorics For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence is called delineation, and more generally holds for circle graphs, rooted directed path graphs, and $H$-graphs when $H$ is a forest. Delineation is based on the key idea that geometric graphs often admit natural vertex orderings, allowing to use the very rich theory of twin-width for ordered graphs. Answering two questions raised in their work, we prove that delineation holds for intersection graphs of non-degenerate axis-parallel unit segment graphs, but fails for visibility graphs of 1.5D terrains. We also prove delineation for intersection graphs of circular arcs. |
| title | First-Order Logic and Twin-Width for Some Geometric Graphs |
| topic | Discrete Mathematics Logic in Computer Science Combinatorics |
| url | https://arxiv.org/abs/2512.21896 |