On computing the smallest four-coloring of planar graphs and non-self-reducible sets in P
نویسندگان
چکیده
We show that computing the lexicographically first four-coloring for planar graphs is ∆p2hard. 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 6= 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 ∆p2hardness can be valuable.
منابع مشابه
A Note on the Complexity of Computing the Smallest Four-Coloring of Planar Graphs
We show that computing the lexicographically first four-coloring for planar graphs is ∆p 2 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 6= NP. We discuss this application to non-self-reducibility and provide a general related result.
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 99 شماره
صفحات -
تاریخ انتشار 2006