A sequence d₁≤⋯≤ dₙ is graphical if it is the degree sequence of a graph. Balister, the second author, Groenland, Johnston and Scott showed that there are asymptotically C4ⁿ/n3/4 such sequences. However, the constant C involves a probability that is only approximated. Using random walks and limit theory for infinitely divisible probability distributions, we describe C in terms of Walkup's formula for the number of rooted, unlabelled and cyclically distinct plane trees.
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Bassan et al. (2024) studied this question.
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