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Abstract
We show that k-uniform hypergraphs on n vertices whose codegree is at least (2/3+o(1))n can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler tours as well. In passing, we also investigate decompositions into tight paths.
In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary k-uniform hypergraphs, which should be of independent interest.
In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary k-uniform hypergraphs, which should be of independent interest.
Original language | English |
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Pages (from-to) | 55-103 |
Number of pages | 49 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 167 |
Early online date | 5 Mar 2024 |
DOIs | |
Publication status | Published - Jul 2024 |
Bibliographical note
Funding:The research leading to these results was supported by ANID-Chile through the FONDECYT Iniciación Nº11220269 grant (N. Sanhueza-Matamala) and EPSRC, grant no. EP/V002279/1 (A. Lo and S. Piga) and EP/V048287/1 (A. Lo). There are no additional data beyond that contained within the main manuscript.
Keywords
- Hypergraphs
- Euler tours
- Cycles
Fingerprint
Dive into the research topics of 'Cycle decompositions in k-uniform hypergraphs'. Together they form a unique fingerprint.Projects
- 2 Finished
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Ramsey theory: an extremal perspective
Treglown, A. (Co-Investigator) & Lo, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/01/22 → 31/12/24
Project: Research Councils
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Matchings and tilings in graphs
Lo, A. (Co-Investigator) & Treglown, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/03/21 → 29/02/24
Project: Research Councils