GRAPHS WITH LEAST NUMBER OF COLORINGS

A lambda-coloring of a graph G is an assignment of lambda or fewer colors to the points of G so that no two adjacent points have the same color. Let Omega(n,e) be the collection of all connected n-point and e-edge graphs and let Omega p(n, e) be the planar graphs of Omega(n, e). This paper characterizes the graphs that minimize the number of lambda-colorings in Omega(n, e) for all lambda greater than or equal to 1 and Omega p(n, e) for all lambda > 4. (C) 1995 John Wiley & Sons, Inc.