Counting unlabeled interval graphs

TL;DR

This paper refines the asymptotic bounds on the number of unlabeled interval graphs with n vertices, showing that their logarithm grows approximately as n log n for large n.

Contribution

It provides improved bounds on the count of unlabeled interval graphs, establishing the asymptotic behavior of their logarithm as n log n.

Findings

log I_n ~ n log n as n approaches infinity

Established tighter bounds on the number of unlabeled interval graphs

Enhanced understanding of the combinatorial complexity of interval graphs

Abstract

We improve the bounds on the number of interval graphs on $n$ vertices. In particular, denoting by $I_n$ the quantity in question, we show that $\log I_n \sim n\log n$ as $n\to \infty$.