Canonical tree-decompositions of chordal graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910189037289472 |
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| author | Jacobs, Raphael W. Knappe, Paul |
| author_facet | Jacobs, Raphael W. Knappe, Paul |
| contents | We show that a locally finite, connected graph $G$ is $r$-locally chordal (that is, its $r/2$-balls are chordal) if and only if the unique canonical graph-decomposition $\mathcal{H}_r(G)$ of $G$ displaying its $r$-global structure is into cliques. Our proof relies on a canonical version of Halin's characterization of chordal locally finite graphs as those that admit a tree-decomposition into cliques: We show that such tree-decompositions can be chosen to be canonical, that is, so that they are invariant under all the graph's automorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical tree-decompositions of chordal graphs Jacobs, Raphael W. Knappe, Paul Combinatorics 05C83, 05C69, 05C40, 05C38 We show that a locally finite, connected graph $G$ is $r$-locally chordal (that is, its $r/2$-balls are chordal) if and only if the unique canonical graph-decomposition $\mathcal{H}_r(G)$ of $G$ displaying its $r$-global structure is into cliques. Our proof relies on a canonical version of Halin's characterization of chordal locally finite graphs as those that admit a tree-decomposition into cliques: We show that such tree-decompositions can be chosen to be canonical, that is, so that they are invariant under all the graph's automorphisms. |
| title | Canonical tree-decompositions of chordal graphs |
| topic | Combinatorics 05C83, 05C69, 05C40, 05C38 |
| url | https://arxiv.org/abs/2512.18480 |