What was already known
Koch and Narayan proved restricted cases and conjectured the broader edge bound for bipartite graphs with a unique minimum dominating set.
AI involvement
Claude agents found the counterexample in John Erlbacher’s directed Demonstrandum campaign. Erlbacher audited its verification gates.
Claude agents supplied the witness under Erlbacher’s direction; individual-result autonomy is not documented.
Importance
Corrects a specific proposed bound in domination theory.
Limitations
The assessment covers this 13-vertex witness. Separate claims about global minimum size or uniqueness up to isomorphism are not included; the source checks both readings of a printed formula typo.
Technical verification
Two clean-room exact checkers reportedly enumerate the graph and its dominating sets, including both readings of a formula typo.
Independent checking
exact computation
- Checker
- cleanroom_check.py and independently written indy_check.py
- Scope
- The 13-vertex γ=4, s=22 witness against Conjecture 1
- Basis
- Reported by the linked checker
Human understanding
No named person explains the individual construction; Few is the evidence default.
Correction and publication history
The 13-vertex witness refutes the stated domination-number bound.
Read this published revision