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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

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Publisher copy:
10.37236/14646

Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0003-4489-5988


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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:

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