Cycle decompositions in $k$-uniform hypergraphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866907822273331200 |
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| author | Lo, Allan Piga, Simón Sanhueza-Matamala, Nicolás |
| author_facet | Lo, Allan Piga, Simón Sanhueza-Matamala, Nicolás |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03564 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cycle decompositions in $k$-uniform hypergraphs Lo, Allan Piga, Simón Sanhueza-Matamala, Nicolás Combinatorics 05C45, 05C65, 05D40 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. |
| title | Cycle decompositions in $k$-uniform hypergraphs |
| topic | Combinatorics 05C45, 05C65, 05D40 |
| url | https://arxiv.org/abs/2211.03564 |