A NEW PROOF OF THE 6 COLOR THEOREM

in 1965 Ringel raised a 6 color problem for graphs that can be stated in at least three different forms. In particular, is it possible to co lor the vertices and faces of every plane graph with 6 colors so that any two adjacent or incident elements are colored differently? This 6 color problem was solved in 1984 by the present author; the proof used about 35 reducible configurations. A shorter new proof is given here using only half as many of reducible configurations. (C) 1995 John Wil ey & Sons, Inc.