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Infinite induced-saturated graphs

Abstract:

A graph G is H-induced-saturated if G is H-free but deleting any edge or adding any edge creates an induced copy of H. There are nontrivial graphs H, such as 𝑃4, for which no finite H-induced-saturated graph G exists. We show that for every finite graph H that is not a clique or an independent set, there always exists a countable H-induced-saturated graph. In fact, we show that a far stronger property can be achieved: there is a countably infinite H-free graph G such that any graph 𝐺′ ≠𝐺 obtained by making a locally finite set of changes to G contains a copy of H.

Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4153/S0008414X26102132

Authors

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


More from this funder
Funder identifier:
https://ror.org/0439y7842
Grant:
EP/X013642/1


Publisher:
Cambridge University Press
Journal:
Canadian Journal of Mathematics More from this journal
Publication date:
2026-03-24
Acceptance date:
2026-02-24
DOI:
EISSN:
1496-4279
ISSN:
0008-414X


Language:
English
Keywords:
Pubs id:
2381245
Local pid:
pubs:2381245
Deposit date:
2026-02-24
ARK identifier:

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