What was already known
The 1995 conjecture was known for co-bipartite graphs and claw-free incomparability graphs. Prajapati found independent counterexamples at about the same time.
AI involvement
Morales asked ChatGPT 5.6 Sol Pro to search; its second attempt found the two graphs using SAT solvers. Matherne and Morales identified their line-graph structure and computed the exact coefficients.
The model found the retained counterexample graphs within a human-chosen search target.
Importance
The explicit graphs settle the universal conjecture, while contemporaneous human examples limit any sole priority claim.
Limitations
The exact coefficients are reported from SageMath computations. Later infinite counterexample families are separate human work.
Technical verification
The finite graph condition follows from line-graph construction and the authors report exact SageMath Schur coefficients for both graphs. This is a source-reported exact computational check, not a locally reproduced run.
Formal checking
Exact finite symbolic coefficient computation plus line-graph construction
- Checker
- Matherne and Morales using SageMath
- Scope
- G1 and G2 have [s_3333] coefficients −64 and −40; both are line graphs and claw-free
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the graphs, coefficient counterexample and relation to known positive graph classes.
Correction and publication history
The explicit graphs settle the universal conjecture, while contemporaneous human examples limit any sole priority claim.
Read this published revision