Displaying prescribed sets of ends by linked tree-decompositions

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.

arXiv comment23 pages, 3 figures