The Vertex Sets of Subtrees of a Tree
Abstract
Let $\mathcal{F}$ be a set of subsets of a set $W$. When is there a tree $T$ with vertex set $W$ such that each member of $\mathcal{F}$ is the set of vertices of a subtree of $T$? It is necessary that $\mathcal{F}$ has the Helly property and the intersection graph of $\mathcal{F}$ is chordal. We will show that these two necessary conditions are together sufficient in the finite case, and more generally, they are sufficient if no element of $W$ belongs to infinitely many infinite sets in $\mathcal{F}$.
Fields of Study & Subjects
Advanced Graph Theory Research
Limits and Structures in Graph Theory
Topological and Geometric Data Analysis
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 2
- Publication date
- 14 April 2026
- Language
- EN