DagSemProc.04421.2.pdf
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Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy
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Dagstuhl Seminar Proceedings, Volume 4421
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2005-03-24
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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
https://doi.org/10.4230/DagSemProc.04421.2
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.
Keywords
- Exact Colorability
- exact domatic number
- boolean hierarchy completeness
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