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Partitioning the vertices of a torus into isomorphic subgraphs

Abstract:

Let H be an induced subgraph of the torus Ckm. We show that when k≥3 is even and |V(H)| divides some power of k, then for sufficiently large n the torus Ckn has a perfect vertex-packing with induced copies of H. On the other hand, disproving a conjecture of Gruslys, we show that when k is odd and not a prime power, then there exists H such that |V(H)| divides some power of k, but there is no n such that Ckn has a perfect vertex-packing with copies of H. We also disprove a conjecture of...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jcta.2020.105252

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0003-4489-5988
Publisher:
Elsevier Publisher's website
Journal:
Journal of Combinatorial Theory, Series A Journal website
Volume:
174
Article number:
105252
Publication date:
2020-03-26
Acceptance date:
2020-03-18
DOI:
EISSN:
1096-0899
ISSN:
0097-3165
Language:
English
Keywords:
Pubs id:
1099399
Local pid:
pubs:1099399
Deposit date:
2020-09-06

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