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math.PR2023★ 1 cited
Critical trees are neither too short nor too fat
Louigi Addario-Berry, Serte Donderwinkel, Igor Kortchemski
We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaymé trees. Our bounds are optimal at this level of generality.…
math.CO2023★ 1 cited
Counting graphic sequences via integrated random walks
Paul Balister, Serte Donderwinkel, Carla Groenland +2
Given an integer , let be the number of integer sequences that are the degree sequence of some graph. We show that $G(n)=(c+o(1))…