Erdős Problem #584

Erdős problem #584 · erdosproblems.com/584

Must every graph with $n$ vertices and $\delta n^2$ edges contain large subgraphs in which every two edges lie on specified short cycles? A dense high-girth construction refutes the statement when $\delta$ may shrink with $n$.

Result

Disproved(see note)

Status

Variant only

AI contribution

AI-discovered

Method

Construction

Field

Extremal Graph Theory

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-13

Model

GPT-5.6 Star Fleet (Claude Fable 5 referee)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article