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Perfect Graphs of Fixed Density: Counting and Homogeneous Sets
Published online by Cambridge University Press: 14 May 2012
Abstract
For c ∈ (0,1) let n(c) denote the set of n-vertex perfect graphs with density c and let
n(c) denote the set of n-vertex graphs without induced C5 and with density c.
We show that
with
otherwise, where H is the binary entropy function.
Further, we use this result to deduce that almost all graphs in n(c) have homogeneous sets of linear size. This answers a question raised by Loebl and co-workers.
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