Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 106-01. Hardness of finding large independent sets in three-colorable graphs
Manuscript map · lines 4555–4564
OpenAI@2026-10-07#rem:oai-p-106-01
Authors: OpenAI. Family 106.
Title: Hardness of finding large independent sets in three-colorable graphs.
Abstract: We prove that, for every fixed $0{}lt {}delta{}lt 1/3$, it is NP-hard to distinguish three-colorable graphs from graphs in which every independent set has fewer than δ times the number of vertices. Consequently, for every fixed integer c ≥ 3, finding a proper c-coloring of a three-colorable graph is NP-hard.
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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