On Universal Cycles of Labeled Graphs

TL;DR

This paper proves the existence of universal cycles for various classes of labeled graphs, providing a compact way to list all objects in these classes efficiently.

Contribution

It establishes the existence of universal cycles across multiple types of labeled graphs, extending previous results to broader graph classes.

Findings

Universal cycles exist for simple graphs, trees, and graphs with multiple edges.

Universal cycles are also proven for directed graphs and hypergraphs.

The results unify and extend prior work on universal cycles in combinatorics.

Abstract

A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with m edges, graphs with loops, graphs with multiple edges (with up to m duplications of each edge), directed graphs, hypergraphs, and k-uniform hypergraphs.