We show that computing the lexicographically first four-coloring for planar graphs is ∆ p 2hard. ... more We show that computing the lexicographically first four-coloring for planar graphs is ∆ p 2hard. This result optimally improves upon a result of Khuller and Vazirani who prove this problem NP-hard, and conclude that it is not self-reducible in the sense of Schnorr, assuming P = NP. We discuss this application to non-self-reducibility and provide a general related result. We also discuss when raising a problem's NP-hardness lower bound to ∆ p 2hardness can be valuable.
We show that computing the lexicographically first four-coloring for planar graphs is ∆ p 2hard. ... more We show that computing the lexicographically first four-coloring for planar graphs is ∆ p 2hard. This result optimally improves upon a result of Khuller and Vazirani who prove this problem NP-hard, and conclude that it is not self-reducible in the sense of Schnorr, assuming P = NP. We discuss this application to non-self-reducibility and provide a general related result. We also discuss when raising a problem's NP-hardness lower bound to ∆ p 2hardness can be valuable.
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