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An AI assisted computation produced a counterexample to a graph coloring method

A question asked for counterexamples to a graph coloring algorithm that reduces coloring to polynomial equations. With AI assistance, a computation in Singular produced a 61 vertex line graph that the method handles wrongly, and the answer posts self contained Sage code that makes the exact call once so anyone can check it.

How it works

  1. The question sets out the algorithm and the graphs already tried
  2. With AI assistance a computation in Singular searches for a breaking case
  3. A 61 vertex line graph counterexample is produced
  4. Self contained verification code is posted with the answer

Why it’s worth knowing

The claim had survived many tried graph families. The AI assisted search found the breaking example and shipped the proof as runnable code.

Where it’s from

Summarized from a public post on mathoverflow.net. See the original ↗

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