What question did this study set out to answer?

The aim is to assess critical cubic vertex-transitive graphs to advance the Erdős–Gyárfás conjecture.

February 16, 2026Open Access

From Cut Localization to Modulus Freeze: Reproducible Empirical Constraints and Theoretical Targets for the Erdős–Gyárfás Conjecture via Matching-Covered Theory

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Empirical audit reveals vertex-transitive graphs and geometric translations impact conjecture outcomes.

The aim is to assess critical cubic vertex-transitive graphs to advance the Erdős–Gyárfás conjecture.
Conducted a reproducible audit of 31 cubic vertex-transitive graphs.
Analyzed properties through matching-covered theory.
Examined arithmetic non-degeneration and conformal length spectrum.
Identified significant gaps in lattice-to-cycle-length systems.
Proposed a modulus-freeze conjecture for proof strategies.
Documented failures in natural geometric translations.

Jonas Jakob Gebendorfer (2026) studied this question.

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