Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 131-01. Polynomial mixing of the switch chain for every graphical degree sequence
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OpenAI@2026-10-07#rem:oai-p-131-01
Authors: OpenAI. Family 131.
Title: Polynomial mixing of the switch chain for every graphical degree sequence.
Abstract: We prove the simple-undirected form of the Kannan–Tetali–Vempala conjecture: the switch chain on simple undirected graphs mixes in polynomial time for every graphical degree sequence. For a lazy chain that proposes switches uniformly on four vertices, the total-variation mixing time at distance 1/4 is at most $2n{}8$. We also give an exactly uniform sampler for every graphical labeled degree vector. It uses unbiased random bits, terminates almost surely, and has expected polynomial bit running time.
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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