Agile Sets in Graphs
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen

TL;DR
This paper characterizes the existence of large agile vertex sets in graphs, linking them to specific minors like $K_{2,k}$ and large strip minors, advancing understanding of graph connectivity properties.
Contribution
It provides a new characterization for large agile sets in graphs based on minors such as $K_{2,k}$ and strip minors, connecting structural graph theory with connectivity concepts.
Findings
Large agile sets are characterized by the presence of $K_{2,k}$ minors.
Large strip minors also indicate the existence of large agile sets.
The results deepen understanding of graph connectivity and minor theory.
Abstract
A set of vertices in a graph is agile if, however we partition the set into two parts, we can always find two vertex-disjoint connected subgraphs where one covers the first and the other the second part. We present a characterization for the existence of large agile sets in terms of and large strip minors.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Optimization and Search Problems
