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Erdős–Gyárfás Conjecture

Prove that every graph with minimum degree at least 3 contains a cycle whose length is a power of two, thereby resolving the Erdős–Gyárfás Conjecture.

References

The conjecture posits that every graph with minimum degree at least 3 contains a cycle whose length is a power of 2.

— Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3 (Carr, 25 Aug 2025) in Section “Discussion and Connections to an Open Problem”, Subsection “Relation to the Erdős–Gyárfás Conjecture”