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arXiv · 2406.05110

Graphical sequences and plane trees

Michal Bassan·Serte Donderwinkel·Brett Kolesnik
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Abstract

Balister, the second author, Groenland, Johnston and Scott recently showed that there are asymptotically $C4^n/n^{3/4}$ many unordered sequences that occur as degree sequences of graphs. Combining limit theory for infinitely divisible distributions with a new bijective connection between a class of random walk trajectories and a subset counting formula from additive number theory, we describe $C$ in terms of Walkup's number of rooted plane trees. The bijection is related to an instance of the L\'evy-Khintchine formula. Our main result complements a result of Stanley, that ordered graphical sequences are related to quasi-forests.

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Michal Bassan, Serte Donderwinkel, Brett Kolesnik. 2024-06-07. Graphical sequences and plane trees. https://doi.org/10.1017/s0963548325100345

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