Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 184-01. Correspondence coloring graphs with a forbidden clique
Manuscript map · lines 5755–5764
OpenAI@2026-10-07#rem:oai-p-184-01
Authors: OpenAI. Family 184.
Title: Correspondence coloring graphs with a forbidden clique.
Abstract: For every fixed integer r ≥ 4, we prove that every Kr-free graph of sufficiently large maximum degree Δ has correspondence chromatic number $O_r({}Delta/{}log{}Delta)$. This resolves the Alon–Krivelevich–Sudakov coloring conjecture in the stronger correspondence-coloring form. The same bound, with a constant depending on F, holds when any fixed graph F is excluded as an ordinary subgraph. Ordinary and list coloring satisfy the same bounds.
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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