The structure of group-labeled graphs forbidding an immersion
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910047089459200 |
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| author | McCarty, Rose McFarland, Caleb Wollan, Paul |
| author_facet | McCarty, Rose McFarland, Caleb Wollan, Paul |
| contents | A $Γ$-labeled graph is an oriented graph with edges invertibly labeled by a group $Γ$. We prove a structure theorem for $Γ$-labeled graphs which forbid a fixed $Γ$-labeled graph as an immersion, for any finite $Γ$. Roughly, we show that such graphs admit a tree-cut decomposition in which every bag either contains few high degree vertices or is nearly signed over a proper subgroup of $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The structure of group-labeled graphs forbidding an immersion McCarty, Rose McFarland, Caleb Wollan, Paul Combinatorics 05C75, 05C83, 05C22 A $Γ$-labeled graph is an oriented graph with edges invertibly labeled by a group $Γ$. We prove a structure theorem for $Γ$-labeled graphs which forbid a fixed $Γ$-labeled graph as an immersion, for any finite $Γ$. Roughly, we show that such graphs admit a tree-cut decomposition in which every bag either contains few high degree vertices or is nearly signed over a proper subgroup of $Γ$. |
| title | The structure of group-labeled graphs forbidding an immersion |
| topic | Combinatorics 05C75, 05C83, 05C22 |
| url | https://arxiv.org/abs/2603.08820 |