PlanarBench: Evaluating LLM Spatial Reasoning via Planar Graph Drawing
Oleksandr Nikitin
cs.CL cs.AI
Abstract
PlanarBench tests whether LLMs can draw planar graphs as ASCII art given only an edge list -- a spatial reasoning task that resists memorization because edge order, edge orientation, and node labels are all permutable. We evaluate 91 models on the 199 simplest non-isomorphic connected planar graphs (2 - 7 vertices). Edge count is the dominant difficulty predictor ($r = -0.85$) -- a finding not reported in prior LLM graph benchmarks, which use only node count as the difficulty axis.
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Classified with taxonomy v2 on Wed, 2 Sept 2026.