Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 174-02. A polynomial-time construction of strong thin trees
Manuscript map · lines 5615–5624
OpenAI@2026-10-07#rem:oai-p-174-02
Authors: OpenAI. Family 174.
Title: A polynomial-time construction of strong thin trees.
Abstract: We give a deterministic polynomial-time construction of strong thin trees. Given a finite k-edge-connected loopless multigraph on at least one vertex, the algorithm constructs a spanning tree meeting every cut in at most a $C/k$ fraction of its edges, for a universal constant C. The running time is polynomial in the binary input length, including when parallel-edge multiplicities are encoded in binary.
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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