@article{BHKMS21locallyspanning,
title = {Rooted Minors and Locally Spanning Subgraphs},
author = {Böhme, Thomas and Harant, Jochen and Kriesell, Matthias and Mohr, Samuel and Schmidt, Jens M},
note = {submitted. },
archivePrefix = {arXiv},
eprint = {2003.04011},
biburl = {http://samuel-mohr.de/files/bib/9.bib},
abstract = {Given a finite, undirected, and simple graph {$G$} and {$X\subseteq V(G)$}, let {$\mathcal{M}$} be a partition of a subset of
{$V(G)$} into connected sets --- called \emph{bags} --- such that each bag contains at most
one vertex of {$X$} and {$X$} is a subset of the union of all bags.
If {$M$} is a simple graph on the vertex set {$\mathcal{M}$} such that there is an edge of {$G$} connecting two bags of {$\mathcal{M}$} if these two bags are adjacent in {$M$}, then {$M$} is an \emph{minor of {$G$} rooted at {$X$}}.
We consider the problem whether {$G$} has a highly connected minor rooted at {$X$} if {$X$} cannot be separated in {$G$} by removing a few vertices of {$G$}.\\
As an application of the achieved results, statements on locally spanning subgraphs of {$G$}, i.\,e.\ subgraphs containing {$X$}, are presented.
},
}