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We introduce a new variant of graph coloring called correspondence coloringwhich generalizes list coloring and allows for reductions previously onlypossible for ordinary coloring. Using this tool, we prove that excluding cyclesof lengths 4 to 8 is sufficient to guarantee 3-choosability of a planar graph,thus answering a question of Borodin.

Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8