Erdős Problem #81

Partial progress by Wouter van Doorn with Aristotle and GPT-5.5 Pro (19 Jun 2026): partial result (Lean).

Problem
Erdős problem #81 (graph theory); current status: open
Credit
Wouter van Doorn with Aristotle and GPT-5.5 Pro · AI working with humans
Checked
Lean formalizationListed in Tao's wiki
Timeline
First AI contribution 2026-06-19 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PARTIALPer Tao's AI-contributions wiki

The problem

Let GG be a chordal graph on nn vertices - that is, GG has no induced cycles of length greater than 33. Can the edges of GG be partitioned into n2/6+O(n)n^2/6+O(n) many cliques?

Statement quoted from erdosproblems.com/81, maintained by Thomas Bloom. Original source: [Er95]. Current status there: open.

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 Humans Outcome
19 Jun, 2026 AI working with humans Aristotle, GPT-5.5 Pro Wouter van Doorn 🟡 Partial result (Lean)

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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