# Efficient enumeration of non-isomorphic interval graphs

## TL;DR

This paper improves the algorithm for enumerating all non-isomorphic interval graphs on n vertices, reducing the time delay from O(n^4) to O(n^3 log n), and extends the catalog for n up to 15.

## Contribution

The authors present a more efficient enumeration algorithm for non-isomorphic interval graphs and provide an extended catalog for small graph sizes.

## Key findings

- Achieved O(n^3 log n) time delay in enumeration
- Extended catalog of non-isomorphic interval graphs up to n=15
- Improved upon previous O(n^4) algorithm

## Abstract

Recently, Yamazaki et al. provided an algorithm that enumerates all non-isomorphic interval graphs on $n$ vertices with an $O(n^4)$ time delay. In this paper, we improve their algorithm and achieve $O(n^3 \log n)$ time delay. We also extend the catalog of these graphs providing a list of all non-isomorphic interval graphs for all $n$ up to $15$.