Faudree–Fronček–Ryjáček–Locke–Langley conjecture on 2-factors in claw-free graphs
Let be a claw-free graph, meaning that has no induced subgraph isomorphic to . Let denote its minimum degree and let denote its independence number. A 2-factor is a -regular spanning subgraph. Faudree et al.'s conjecture. If
then has a -factor with exactly cycles. This conjecture proposes a substantially smaller minimum-degree condition than earlier sufficient conditions; the source states that the bound cannot be improved for existence of such a 2-factor, but does not state that the conjecture itself has been resolved.
References
Primary source
Masaki Kashima, “Degree sum conditions and a 2-factor with a bounded number of cycles in claw-free graphs”, arXiv:2504.08268 (2025).
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