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arXiv · 2603.08820

The structure of group-labeled graphs forbidding an immersion

Rose McCarty·Caleb McFarland·Paul Wollan
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Abstract

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 $Γ$.

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BibTeXRIS

Rose McCarty, Caleb McFarland, Paul Wollan. 2026-03-09. The structure of group-labeled graphs forbidding an immersion. https://arxiv.org/abs/2603.08820

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