Graph colorings belong to the most important optimization problems of applied graph theory, and at the same time provide a rich source of directions of theoretical research. E.g., the Four Color Conjecture has influenced research for decades. In the last 20 years extensions of the chromatic theory such as precoloring extension, list colorings and chooseability of graphs have been introduced and widely studied. These concepts will be defined in the talk and several results namely on planar graphs will be presented.
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