Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 181-01. A linear cycle-and-edge decomposition of every graph
Manuscript map · lines 5705–5714
OpenAI@2026-10-07#rem:oai-p-181-01
Authors: OpenAI. Family 181.
Title: A linear cycle-and-edge decomposition of every graph.
Abstract: We prove that every finite simple undirected graph on n vertices has an edge partition into at most $Cn$ simple cycles and single edges, for an absolute constant C. This resolves the Erdős–Gallai cycle decomposition conjecture positively.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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