A Note on the Complexity of Computing the Smallest Four-Coloring of Planar Graphs

Andre Grosse; Joerg Rothe; Gerd Wechsung

A Note on the Complexity of Computing the Smallest Four-Coloring of Planar Graphs

Computational Complexity 2007-05-23 v2

Authors: Andre Grosse , Joerg Rothe , Gerd Wechsung

Abstract

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 \neq NP. We discuss this application to non-self-reducibility and provide a general related result.

Keywords

four-coloring planar graphs P^{NP}-hard lexicographically first coloring non-self-reducible

Cite

@article{arxiv.cs/0106045,
  title  = {A Note on the Complexity of Computing the Smallest Four-Coloring of Planar Graphs},
  author = {Andre Grosse and Joerg Rothe and Gerd Wechsung},
  journal= {arXiv preprint arXiv:cs/0106045},
  year   = {2007}
}

Comments

9 pages, appears in part in an ICTCS 2001 paper by the same authors, minor revision of the above

A Note on the Complexity of Computing the Smallest Four-Coloring of Planar Graphs

Abstract

Keywords

Cite

Comments

Related papers