Erdős Problem #593

Erdős problem #593 · erdosproblems.com/593

Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Infinite Hypergraph Theory

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-23

Model

ChatGPT + Aristotle

Vendor

OpenAI / Harmonic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article