Remark: Family 181. The Erd (o)s–Gallai cycle-decomposition conjecture

Proves that the edges of every finite simple undirected graph on $n$ vertices can be partitioned into at most $Cn$ simple cycles and single edges, for an absolute constant $C$. This resolves the Erdős–Gallai cycle-decomposition conjecture, bounding the number of pieces linearly even for dense graphs.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.