The Papamanthou-Tollis Conjecture on Parameterized st-Orientations

On the basis of experiments up to 5000 nodes, Papamanthou and Tollis conjectured a relation between the longest paths produced by their MaxSTN and MinSTN algorithms for $st$-orientations of biconnected graphs. A counterexample refutes it.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jun 12, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: The Papamanthou-Tollis Conjecture on Parameterized st-Orientations · st-orientations

Confidence: Not scored

Registry verification: site confirmed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Charalampos Papamanthou
human · human collaborator

Claude Sonnet 4.6
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The Papamanthou-Tollis Conjecture on Parameterized st-Orientations

specialist registry · passed

The refutation is an explicit graph, so it reduces to running the two named algorithms on it, and that part stands on its own. The surrounding computational claims deserve less weight: in the same section the authors record that the model produced counterexamples later confirmed wrong, and that they did not verify its claim to have exhaustively searched the biconnected graphs on five and six vertices. arXiv note, not peer-reviewed.

Source ↗

The Papamanthou-Tollis Conjecture on Parameterized st-Orientations

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lineage and corrections

This event attributed to Charalampos Papamanthou

This event attributed to Claude Sonnet 4.6

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