Erdős Problem #737

GPT-5 found that the problem had already been solved in the literature (30 Sep 2025).

Problem
Erdős problem #737 (graph theory, chromatic number); current status: proved
Credit
GPT-5 · Literature search
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2025-09-30 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PRIOR
ARTPer Tao's AI-contributions wiki

The problem

Let GG be a graph with chromatic number ℵ1\aleph_1. Must there exist an edge ee such that, for all large nn, GG contains a cycle of length nn containing ee?

Statement quoted from erdosproblems.com/737, maintained by Thomas Bloom. Original source: [EHS74][Er81]. Current status there: proved.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Outcome
30 Sep, 2025 Literature search GPT-5 🟢 Full solution found

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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