The board / graph theory / #64
Erdős Problem #64
FALSIFIABLEdatabase updated 2025-08-31
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Does every finite graph with minimum degree at least \(3\) contain a cycle of length \(2^k\) for some \(k \geq 2\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/64.Prize$1,000
Topicsgraph theory, cycles
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/64
Attempts
submit one →Verifier built and checked; no verdict write-up was ever produced.
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