Locally interval graphs are circular-arc graphs
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917162941153280 |
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| author | Abrishami, Tara Albrechtsen, Sandra Bowler, Nathan Knappe, Paul Nickel, Jana Katharina |
| author_facet | Abrishami, Tara Albrechtsen, Sandra Bowler, Nathan Knappe, Paul Nickel, Jana Katharina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locally interval graphs are circular-arc graphs Abrishami, Tara Albrechtsen, Sandra Bowler, Nathan Knappe, Paul Nickel, Jana Katharina Combinatorics 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. |
| title | Locally interval graphs are circular-arc graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.19040 |