Planar graph coloring is not self-reducible, assuming P ≠ NP
نویسندگان
چکیده
منابع مشابه
Planar Graph Coloring is not Self-Reducible, Assuming P != NP
We show that obtaining the lexicographically first four coloring of a planar graph is NP–hard. This shows that planar graph four-coloring is not self-reducible, assuming P 6= NP . One consequence of our result is that the schema of [JVV 86] cannot be used for approximately counting the number of four colorings of a planar graph. These results extend to planar graph k-coloring, for k ≥ 4. Resear...
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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 rai...
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We show that the game chromatic number of a planar graph is at most 33. More generally, there exists a function f: f\l --+ f\l so that for each n E f\l. if a graph does not contain a homeomorph of Kn• then its game chromatic number is at most f(n). In particular, the game chromatic number of a graph is bounded in terms of its genus. Our proof is motivated by the concept of p-arrangeability, whi...
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A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of NPT(NP) ∩ P/Poly. In this paper, we show that NE 6⊆ NPT(NP ∩ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c > 0, |A| ≤ 2 c for infinitely many integers n). Our result implies NE 6⊆ N...
متن کاملNE is not NP Turing Reducible to Nonexpoentially Dense NP Sets
A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of NPT(NP) ∩ P/Poly. In this paper, we show that NE 6⊆ NPT(NP ∩ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c > 0, |A≤n| ≤ 2nc for infinitely many integers n). Our result implies NE 6⊆...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1991
ISSN: 0304-3975
DOI: 10.1016/0304-3975(91)90081-c