Dirac's map-color theorem for choosability

It is proved that the choice number of every graph G embedded on a surface of Euler genus epsilon greater than or equal to 1 and epsilon not equal 3 i s at most the Heawood number H(epsilon) = [(7 + root 24 epsilon + 1)/2] and that the equality holds if and only if G contains the complete graph K-H(e psilon) as a subgraph. (C) 1999 John Wiley Br Sons, Inc. J Graph Theory 32: 327-339, 1999.