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2 votes

Hardness of Maximum Independent Set in 3-Colorable Graphs

As detailed below, the problem of finding an independent set of size $\Omega(n^{1-\delta})$ in 3-colorable graphs is essentially equivalent to $O(n^\delta)$-approximating 3-COLOR. Currently, the best ...
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13 votes

Is the 3-coloring problem NP-hard on graphs of maximal degree 3?

The answer is no: the 3-coloring problem can be solved in linear time on graphs of maximal degree 3 or less, by application of Brooks' theorem. I wasted some time figuring this out, so I thought I'd ...
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