Geodesic
Graph colorings with local constraints - a survey
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 161-228

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We survey the literature on those variants of the chromatic number problem where not only a proper coloring has to be found (i.e., adjacent vertices must not receive the same color) but some further local restrictions are imposed on the color assignment. Mostly, the list colorings and the precoloring extensions are considered.
Keywords: graph coloring, list coloring, choice number, precoloring extension, complexity of algorithms, chromatic number 
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     author = {Tuza, Zsolt},
     title = {Graph colorings with local constraints - a survey},
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Tuza, Zsolt. Graph colorings with local constraints - a survey. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 161-228. http://geodesic.mathdoc.fr/item/DMGT_1997_17_2_a0/