Displaying prescribed sets of ends by linked tree-decompositions

Sandra Albrechtsen; Max Pitz; Roman Schaut

Displaying prescribed sets of ends by linked tree-decompositions

Combinatorics 2025-12-16 v1

Authors: Sandra Albrechtsen , Max Pitz , Roman Schaut

Abstract

We show that if a subset $\Psi$ of the ends of a graph $G$ can be displayed by a tree-decomposition of finite adhesion, then it can also be displayed by a linked such tree-decomposition. This tree-decomposition captures all combinatorial information of the ends in $\Psi$ : their degrees, their sets of dominating vertices, and their combined degrees.

Keywords

tree-decomposition graph ends linked tree-decomposition finite adhesion dominating vertices

Cite

@article{arxiv.2512.13457,
  title  = {Displaying prescribed sets of ends by linked tree-decompositions},
  author = {Sandra Albrechtsen and Max Pitz and Roman Schaut},
  journal= {arXiv preprint arXiv:2512.13457},
  year   = {2025}
}

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23 pages, 3 figures

Displaying prescribed sets of ends by linked tree-decompositions

Abstract

Keywords

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