This article shows that the vertices of a plane triangulation may be c
olored with 10 colors such that every pair of vertices has different c
olors if they are either adjacent or diagonal, that is, that they are
not adjacent but are adjacent to two faces which share an edge, This i
mproves a result of Borodin, who showed that 11 colors were sufficient
. (C) 1995 John Wiley and Sons, Inc.