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Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy

Author Jörg Rothe

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  • Exact Colorability
  • exact domatic number
  • boolean hierarchy completeness

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Abstract

This talk surveys some of the work that was 
inspired by Wagner's general technique to prove 
completeness in the levels of the boolean 
hierarchy over NP.  In particular, we show that 
it is DP-complete to decide whether or not a 
given graph can be colored with exactly four 
colors.  DP is the second level of the boolean 
hierarchy.  This result solves a question raised
by Wagner in his 1987 TCS paper; its proof uses a
clever reduction by Guruswami and Khanna.  
Similar results on various versions of the exact 
domatic number problem are also discussed.
The result on Exact-Four-Colorability appeared 
in IPL, 2003.  The results on exact domatic 
number problems, obtained jointly with Tobias
Riege, are to appear in TOCS.

Cite As Get BibTex

Jörg Rothe. Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy. In Algebraic Methods in Computational Complexity. Dagstuhl Seminar Proceedings, Volume 4421, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005) https://doi.org/10.4230/DagSemProc.04421.2

Author Details

Jörg Rothe
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