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

We introduce a new variant of graph coloring called correspondence coloring\nwhich generalizes list coloring and allows for reductions previously only\npossible for ordinary coloring. Using this tool, we prove that excluding cycles\nof lengths 4 to 8 is sufficient to guarantee 3-choosability of a planar graph,\nthus answering a question of Borodin.\n