Colouring, constraint satisfaction, and complexity

10 years 6 months ago
Colouring, constraint satisfaction, and complexity
Constraint satisfaction problems have enjoyed much attention since the early seventies, and in the last decade have become also a focus of attention amongst theoreticians. Graph colourings are a special class of constraint satisfaction problems; they offer a microcosm of many of the considerations that occur in constraint satisfaction. From the point of view of theory, they are well known to exhibit a dichotomy of complexity - the k-colouring problem is polynomial time solvable when k 2, and NP-complete when k 3. Similar dichotomy has been proved for the class of graph homomorphism problems, which are intermediate problems between graph colouring and constraint satisfaction. However, for general constraint satisfaction problems, dichotomy has only been conjectured. Although the conjecture remains unproven to this day, it has been driving much of the theoretical research on constraint satisfaction problems, which combines methods of logic, universal algebra, analysis, and combinatori...
Pavol Hell, Jaroslav Nesetril
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where CSR
Authors Pavol Hell, Jaroslav Nesetril
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