Journal article
The vertex sets of subtrees of a tree
- Abstract:
- Let $F$ be a set of subsets of a set $W$. When is there a tree $T$ with vertex set $W$ such that each member of $F$ is the set of vertices of a subtree of $T$? It is necessary that $F$ has the Helly property and the intersection graph of $F$ 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 $F$.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, pdf, 278.9KB, Terms of use)
-
- Publisher copy:
- 10.37236/14646
Authors
+ Engineering and Physical Sciences Research Council
More from this funder
- Funder identifier:
- https://ror.org/0439y7842
- Grant:
- EP/X013642/1
- 2884208
- Publisher:
- Electronic Journal of Combinatorics
- Journal:
- Electronic Journal of Combinatorics More from this journal
- Volume:
- 33
- Issue:
- 2
- Article number:
- P2.7
- Publication date:
- 2026-04-14
- Acceptance date:
- 2026-03-12
- DOI:
- EISSN:
-
1077-8926
- Language:
-
English
- Pubs id:
-
2388909
- Local pid:
-
pubs:2388909
- Deposit date:
-
2026-03-13
- ARK identifier:
Terms of use
- Copyright holder:
- Chudnovsky et al
- Copyright date:
- 2025
- Rights statement:
- © 2025 The authors. Released under the CC BY-ND license (International 4.0).
- Licence:
- CC Attribution (CC BY)
If you are the owner of this record, you can report an update to it here: Report update to this record