Displaying prescribed sets of ends by linked tree-decompositions

TL;DR

This paper proves that for certain graph ends, a linked tree-decomposition can display all their combinatorial properties, enhancing understanding of graph structure related to ends.

Contribution

It demonstrates that ends displayable by finite-adhesion tree-decompositions can also be displayed by linked ones, preserving all combinatorial information.

Findings

Linked tree-decompositions can display all ends with finite adhesion.

They capture degrees, dominating vertices, and combined degrees of ends.

The result improves structural understanding of graph ends.

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.