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math.CO2025
On the chromatic number of random triangle-free graphs
Clayton Mizgerd, Will Perkins, Yuzhou Wang
We study the chromatic number of typical triangle-free graphs with edges and establish the width of the scaling window for the transitions…
math.CO2025
The typical structure of dense claw-free graphs
Will Perkins, Sam van der Poel
We analyze the asymptotic number and typical structure of claw-free graphs at constant edge densities. The first of our main results is a formula for the asymptotics of the logarit…