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Abstract

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 Gn of triangle-free graphs with X(Gn) = n. In this article, we calculate the fractional chromatic number of Gn and show that this sequence of numbers satisfies the unexpected recurrence an+1 = an + (1/an). © 1995 John Wiley & Sons, Inc.