Power-of-two cycles in graphs covered by pentagons
Year: 2026
Type: preprint
Abstract: We prove two special cases of the Erdős–Gyárfás conjecture. Every finite simple graph of minimum degree at least three with a spanning factor of pentagons contains a simple cycle whose length is a power of two. For cubic graphs, it suffices that every vertex lie on a pentagon, allowing overlap. The preprint includes proofs, a finite verification appendix, and a reproducible Python checker in the source archive. The manuscript documents the use of AI in its preparation.
Author: Jiang, Weiqi
Institutions: Chinese Academy of Sciences, Institute of Theoretical Physics
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225627138
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