Title: PlanarBench: Assessing LLM Spatial Reasoning Through Planar Graph Drawing

Abstract: PlanarBench is designed to test whether large language models can generate ASCII art representations of planar graphs when provided solely with an edge list. This specific spatial reasoning challenge is resistant to rote memorization, as the permutation of edge order, node labels, and edge orientation ensures variability. In this study, we assessed 91 distinct models using the 199 simplest non-isomorphic connected planar graphs, which range from 2 to 7 vertices. Our analysis reveals that the number of edges is the primary predictor of difficulty ($r = -0.85$). This insight diverges from previous LLM graph benchmarks, which have relied exclusively on node count to determine task difficulty.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC