A Note on the Complexity of Computing the Smallest Four-Coloring of Planar Graphs
André Große, Rothe, Joerg, Gerd Wechsung · arXiv (Cornell University) · 2001
We show that computing the lexicographically first four-coloring for planar graphs is P^{NP}-hard. This result optimally improves upon a result of Khuller and Vazirani who prove this problem to be NP-hard, and conclude that it is not self-reducible in the sense of Schnorr, assuming P eq NP. We discuss this application to non-self-reducibility and provide a general related result.