AI Chat AI Image Generator AI Video Text to Speech

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

06/21/2001

∙

by André Grosse, et al.

∙

∙

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

André Grosse
2 publications
Joerg Rothe
4 publications
Gerd Wechsung
2 publications

page 1

page 2

page 3

page 4

research

∙ 04/17/2021

3-Coloring on Regular, Planar, and Ordered Hamiltonian Graphs

We prove that 3-Coloring remains NP-hard on 4- and 5-regular planar Hami...

0 Dario Cavallaro, et al. ∙

research

∙ 10/13/2020

Digraph Coloring and Distance to Acyclicity

In k-Digraph Coloring we are given a digraph and are asked to partition ...

0 Ararat Harutyunyan, et al. ∙

research

∙ 06/24/2021

Kemeny ranking is NP-hard for 2-dimensional Euclidean preferences

The assumption that voters' preferences share some common structure is a...

0 Bruno Escoffier, et al. ∙

research

∙ 08/27/2018

Fair redistricting is hard

Gerrymandering is a long-standing issue within the U.S. political system...

0 Richard Kueng, et al. ∙

research

∙ 12/04/2018

Rigid Foldability is NP-Hard

In this paper, we show that deciding rigid foldability of a given crease...

0 Hugo Akitaya, et al. ∙

research

∙ 09/20/2022

VEST is W[2]-hard

In this short note, we show that the problem of VEST is W[2]-hard for pa...

0 Michael Skotnica, et al. ∙

research

∙ 09/05/2018

Computing the Difficulty of Critical Bootstrap Percolation Models is NP-hard

Bootstrap percolation is a class of cellular automata with random initia...

0 Ivailo Hartarsky, et al. ∙