lean artifact · pending
Artifact ↗Source authenticated
Gyarfas's conjecture on covering edge-colored complete graphs by r-1 monochromatic trees
For every sufficiently large prime (September 27 paper), and for with a large prime and large odd (September 23 paper), there is a finite complete graph with an -edge-coloring whose vertices need exactly monochromatic trees to cover them; the same holds for connected monochromatic subgraphs. Built from the Ryser counterexamples by coloring each pair of hyperedges by a part where they meet. Not addressed: small , or the distinct vertex-disjoint tree-partition conjecture of Erdos-Gyarfas-Pyber.
Exact FrontierDelta
Prior state unknown→disproved
Scope and record
Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Gyarfas's conjecture on covering edge-colored complete graphs by r-1 monochromatic trees · Gyarfas tree-cover conjecture
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Companion: Balanced counterexamples to Ryser's conjecture at prime orders (September 27, 2026) evidence for this event
This event attributed to Unreleased internal OpenAI model
For every sufficiently large prime (September 27 paper), and for with a large prime and large odd (September 23 paper), there is a finite complete graph with an -edge-coloring whose vertices need exactly monochromatic trees to cover them; the same holds for connected monochromatic subgraphs. Built from the Ryser counterexamples by coloring each pair of hyperedges by a part where they meet. Not addressed: small , or the distinct vertex-disjoint tree-partition conjecture of Erdos-Gyarfas-Pyber. parent of this event
Lean proof: OAI/Combinatorics/Ryser/OddExtensions.lean evidence for this event
Erdos, Gyarfas, Pyber, Vertex coverings by monochromatic cycles and trees (JCTB 1991) evidence for this event
VibeMathed record: Gyarfas's conjecture on covering edge-colored complete graphs by r-1 monochromatic trees evidence for this event
Gyarfas's conjecture on covering edge-colored complete graphs by r-1 monochromatic trees parent of this event
Gyarfas's conjecture on covering edge-colored complete graphs by r-1 monochromatic trees evidence for this event
Lean proof: OAI/Combinatorics/Ryser/Construction/Main.lean evidence for this event
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