## 24 Citations

Complexity of the Exact Domatic Number Problem and of the Exact Conveyor Flow Shop Problem

- MathematicsProceedings. 2004 International Conference on Information and Communication Technologies: From Theory to Applications, 2004.
- 2004

It is proved that the exact versions of the domatic number problem are complete for the levels of the Boolean hierarchy over NP, the 2kth level of the boolean hierarchy overNP.

Completeness in the Boolean Hierarchy: Exact-Four-Colorability, Minimal Graph Uncolorability, and Exact Domatic Number Problems - a Survey

- MathematicsJ. Univers. Comput. Sci.
- 2006

It is shown that it is DP-complete to decide whether or not a given graph can be colored with exactly four colors, where DP is the second level of the boolean hierarchy.

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

- MathematicsInf. Process. Lett.
- 2006

Complexity of Stability

- Computer ScienceISAAC
- 2020

Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to…

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

- MathematicsArXiv
- 2001

It is shown that computing the lexicographically first four-coloring for planar graphs is P^{NP}-hard, and it is concluded that it is not self-reducible in the sense of Schnorr, assuming P \neq NP.

C C ] 1 O ct 2 01 9 Complexity of Stability

- Computer Science, Mathematics
- 2019

Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to…

Exact Complexity of Exact-Four-Colorability and of the Winner Problem for Young Elections

- MathematicsIFIP TCS
- 2002

A general result is proved that in particular solves Wagner’s question in the affirmative about whether it is DP-complete to determine if the chromatic number of a given graph is exactly four.

Introduction to Computational Complexity ∗ — Mathematical Programming Glossary Supplement —

- Computer Science
- 2010

The foundations of complexity theory are described, upper bounds on the time complexity of selected problems are surveyed, the notion of polynomial-time many-one reducibility as a means to obtain lower bound results, and NP-completeness and the P-versus-NP question are discussed.

EFFICIENT APPROXIMATIONS OF CONJUNCTIVE

- Computer Science, Mathematics
- 2014

This paper defines approximations of a given query Q as queries from one of those classes that disagree with Q as little as possible, and proves that for the above classes of tractable conjunctive queries, approximation always exist and are at most polynomial in the size of the original query.

Efficient approximations of conjunctive queries

- Computer Science, MathematicsPODS '12
- 2012

It is proved that for the above classes of tractable conjunctive queries, approximations always exist, and are at most polynomial in the size of the original query.

## References

SHOWING 1-10 OF 35 REFERENCES

On the Hardness of 4-Coloring a 3-Colorable Graph

- MathematicsSIAM J. Discret. Math.
- 2000

A new proof showing that it is NP-hard to color a 3-colorable graph using just 4 colors is given, and it is pointed out that such graphs can always be colored using O(1) colors by a simple greedy algorithm, while the best known algorithm for coloring (general) 3- colorable graphs requires $n^{\Omega(1)}$ colors.

On the Hardness of Approximating the Chromatic Number

- MathematicsComb.
- 2000

It is NP-hard to find a 4-coloring of a 3-chromatic graph and as an immediate corollary it is obtained that it isNP- hard to color a k- chromatic graph with at most colors.

Complexity of the Exact Domatic Number Problem and of the Exact Conveyor Flow Shop Problem

- MathematicsProceedings. 2004 International Conference on Information and Communication Technologies: From Theory to Applications, 2004.
- 2004

It is proved that the exact versions of the domatic number problem are complete for the levels of the Boolean hierarchy over NP, the 2kth level of the boolean hierarchy overNP.

On the hardness of 4-coloring a 3-collorable graph

- MathematicsProceedings 15th Annual IEEE Conference on Computational Complexity
- 2000

A new proof is given showing that it is NP-hard to color a 3-colorable graph using just four colors, and it is pointed out that such graphs can always be colored using O(1) colors by a simple greedy algorithm, while the best known algorithm for coloring (general) 3-colored graphs requires n/sup /spl Omega/(1)/ colours.

Planar 3-colorability is polynomial complete

- MathematicsSIGA
- 1973

The general problem of recognizing the set of pairs (G,k), where k is a positive integer and G is a graph which is k-colorable, is polynomial complete as defined by Karp [I]. It is shown here that…

Some Simplified NP-Complete Graph Problems

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1976

Graph Minimal Uncolorability is D^P-Complete

- MathematicsSIAM J. Comput.
- 1987

It is shown that minimal-3-uncolorability is D-p-complete, for all fixed $k \geq 3$, and can be modified by using ``sensitive'' gadgets to resolve the planar case, bounded vertex degree case and their combination.

Unambiguous Computation: Boolean Hierarchies and Sparse Turing-Complete Sets

- Computer ScienceSIAM J. Comput.
- 1997

It is shown that two hierarchies---the Hausdorff hierarchy and the nested difference hierarchy---which in the NP case are equal to the Boolean closure fail to be equal for the UP case in some relativized worlds, and it is proved that closure under union is not needed for this claim.

More Complicated Questions About Maxima and Minima, and Some Closures of NP

- MathematicsTheor. Comput. Sci.
- 1987

Bounded Queries to SAT and the Boolean Hierarchy

- Computer Science, MathematicsTheor. Comput. Sci.
- 1991