The board / graph theory / #58
Erdős Problem #58
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(G\) is a graph which contains odd cycles of \(\leq k\) different lengths then \(\chi(G)\leq 2k+2\), with equality if and only if \(G\) contains \(K_{2k+2}\). Conjectured by Bollobás and Erdős. Proved by Gyárfás [Gy92].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/58.Prizenone
Topicsgraph theory, chromatic number, cycles
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/58
Attempts
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