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SIAM J. on Computing / Volume 38 / Issue 5

SIAM J. Comput. 38, pp. 1782-1802 (21 pages)

The CSP Dichotomy Holds for Digraphs with No Sources and No Sinks (A Positive Answer to a Conjecture of Bang-Jensen and Hell)

Libor Barto, Marcin Kozik, and Todd Niven

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Bang-Jensen and Hell conjectured in 1990 (using the language of graph homomorphisms) a constraint satisfaction problem (CSP) dichotomy for digraphs with no sources or sinks. The conjecture states that the CSP for such a digraph is tractable if each component of its core is a cycle and is $NP$-complete otherwise. In this paper we prove this conjecture and, as a consequence, a conjecture of Bang-Jensen, Hell, and MacGillivray from 1995 classifying hereditarily hard digraphs. Further, we show that the CSP dichotomy for digraphs with no sources or sinks agrees with the algebraic characterization conjectured by Bulatov, Jeavons, and Krokhin in 2005.

© 2009 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

68R10, 08A70

PUBLICATION DATA

ISSN

0097-5397 (print)  
1095-7111 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received November 14, 2007
Accepted August 01, 2008
Published online January 09, 2009
Digital Object Identifier
http://dx.doi.org/10.1137/070708093

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