For every fixed 0<δ<1/3, it is NP-hard to distinguish three-colorable finite simple graphs from graphs whose largest independent set has fewer than δ times the vertices.
For every fixed 0<δ<1/3, it is NP-hard to distinguish three-colorable finite simple graphs from graphs whose largest independent set has fewer than δ times the vertices.
For every fixed 0<δ<1/3, it is NP-hard to distinguish three-colorable finite simple graphs from graphs whose largest independent set has fewer than δ times the vertices.
If correct, strengthens the hardness of approximating coloring on three-colorable graphs and implies that finding any fixed c-coloring, c≥3, is NP-hard under this promise.
Is the large-independent-set gap NP-hard under three-colorability?
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OpenAI reports hardness of large independent sets in three-colorable graphs
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