Dinitz-Garg-Goemans Conjecture

For single-source unsplittable flow, every fractional flow can be rounded to an unsplittable flow whose cost is no higher than the fractional cost, while each arc's load is exceeded by at most the maximum demand. (The cost version of Goemans' unsplittable-flow conjecture.)

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 22, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Dinitz-Garg-Goemans Conjecture · Dinitz-Garg-Goemans

Confidence: Not scored

Registry verification: unreviewed · announcement · resolved

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Attribution

VibeMathed
registry · event recorded by

Dmitry Rybin
human · human collaborator

GPT-5.6 Pro
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Dinitz-Garg-Goemans Conjecture

specialist registry · passed

Announced on X by Dmitry Rybin (2026-07-22) with a shared GPT-5.6 Pro chat. The counterexample is a concrete finite graph checkable by direct computation (fractional cost 58 vs. minimum unsplittable cost 60 under capacity violation $\le 15$), but it is not yet peer-reviewed or formally verified. Not to be confused with the separate 'Dinitz conjecture' on Latin-square colourings.

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Dinitz-Garg-Goemans Conjecture

witness · pending

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

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Related VibeMathed entry: four-terminal planar DGG counterexample

specialist registry · pending

independent link supplied by the VibeMathed registry.

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Lineage and corrections

This event attributed to Dmitry Rybin

This event attributed to GPT-5.6 Pro

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