THE FRACTIONAL CHROMATIC NUMBER OF MYCIELSKIS GRAPHS

The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence G(n) of triangle-free graphs with chi(G(n)) = n. In this article, we calculate the fractional chromatic number of G, and show that this sequence of numbers satisfies the unexpected recurrence a(n+1) = a(n) + (1/a(n)). (C) 1995 John Wiley & Sons, Inc.