The fractional chromatic number of mycielski's graphs

James Propp 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 X(G_n) = n. In this article, we calculate the fractional chromatic number of G_n and show that this sequence of numbers satisfies the unexpected recurrence a_n+1 = a_n + (1/a_n). © 1995 John Wiley & Sons, Inc.