Locally interval graphs are circular-arc graphs
Combinatorics
2025-12-23 v1
Abstract
Circular-arc graphs are graphs that can be represented as intersection graphs of subpaths of a cycle. Interval graphs are graphs that can be represented as intersection graphs of subpaths of a path. Since cycles are locally paths, every circular-arc graph is locally interval. In this paper, we prove that the converse holds as well: every locally interval graph is a circular-arc graph. This result and its proofs are connected to a recent broader study of structural local-global theory and build on previous work on locally chordal graphs.
Keywords
Cite
@article{arxiv.2512.19040,
title = {Locally interval graphs are circular-arc graphs},
author = {Tara Abrishami and Sandra Albrechtsen and Nathan Bowler and Paul Knappe and Jana Katharina Nickel},
journal= {arXiv preprint arXiv:2512.19040},
year = {2025}
}
Comments
The results in this paper first appeared in arXiv:2501.17320v1 which is now split into four separate papers