The board / graph theory / #705
Erdős Problem #705
DISPROVEDdatabase updated 2026-01-27
The statement as posed is false.
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Let \(G\) be a finite unit distance graph in \(\mamthbb{R}^2\). Is there some \(k\) such that if \(G\) has girth \(≥ k\), then \(\chi(G) ≤ 3\)? The general case was solved by O'Donnell [OD99], who constructed finite unit distance graphs with chromatic number \(4\) and arbitrarily large girth.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/705.Prizenone
Topicsgraph theory, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/705
Attempts
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