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May 29, 2026Open Access

First-Order Logic and Twin-Width for Some Geometric Graphs

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Authors

CGColin GenietGKGunwoo KimLMLucas Meijer

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Overview

Randomized trial explores first-order logic tractability in geometric graph classes, indicating various delineation results.

Key Points

  • This research aims to characterize the tractability of testing first-order formulas in specific geometric graph classes based on twin-width.
  • Examined delineation in intersection graphs of non-degenerate axis-parallel unit segment graphs and visibility graphs of 1.5D terrains.
  • Studied intersection graphs of circular arcs to establish delineation properties.
  • Utilized theoretical frameworks of twin-width and ordered graphs for analysis.
  • Delineation confirmed for intersection graphs of non-degenerate axis-parallel unit segment graphs.
  • Delineation does not hold for visibility graphs of 1.5D terrains.
  • Delineation established for intersection graphs of circular arcs.

Cite This Study

Geniet et al. (2026) studied this question.

synapsesocial.com/papers/6a192f88fab5b468c4418b7dhttps://doi.org/10.4230/lipics.socg.2026.51
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