What question did this study set out to answer?

The aim is to explore the reconfiguration geometry of known Ramsey (5,5,42) graphs and the defect-one closure reachable from them.

August 3, 2026Open Access

Defect-One Closure and Reconfiguration Geometry of the Known Ramsey (5,5,42) Graphs: Technical Report and Reproducibility Package

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Computational study reveals defect-one closures in Ramsey (5,5,42) graphs, implying barriers to undiscovered classes.

The aim is to explore the reconfiguration geometry of known Ramsey (5,5,42) graphs and the defect-one closure reachable from them.
Conducted AI-assisted computational analysis of 656 isomorphism classes of Ramsey (5,5,42) graphs.
Explored single-edge additions and deletions to understand structural barriers and reachable graphs.
Developed a reproducibility package including source code and documentation for verification.
Identified 8,284 reachable isomorphism classes with 33,154 quotient edges from known graphs.
No additional defect-zero classes found under single-edge modifications maintaining defect one.
Classified the reconfiguration landscape into 12 connected components forming various graph types.

Lyu et al. (2026) studied this question.

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