On computing the smallest four-coloring of planar graphs and non-self-reducible sets in P

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. Key words: computational complexity, graph colorability, self-reducibility

• Type: Journal
• Year: 2006
• Where: IPL
• Authors: André Große, Jörg Rothe, Gerd Wechsung
• Keywords: IPL 2006, Lexicographically, Planar Graphs, Vazirani