Spectrum of $3$-uniform $6$- and $9$-cycle systems over $K_v^{(3)}-I$
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911892285423616 |
|---|---|
| author | Keszler, Anita Tuza, Zsolt |
| author_facet | Keszler, Anita Tuza, Zsolt |
| contents | We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if $v\equiv 0,3,6$ (mod 12) and $v\geq 6$; and a decomposition into tight 9-cycles exists for all $v\geq 9$ divisible by 3. These results are complementary to the theorems of Akin et al. [Discrete Math. 345 (2022)] and Bunge et al. [Australas. J. Combin. 80 (2021)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11058 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Spectrum of $3$-uniform $6$- and $9$-cycle systems over $K_v^{(3)}-I$ Keszler, Anita Tuza, Zsolt Combinatorics 05C65, 05C51, 05C38 We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if $v\equiv 0,3,6$ (mod 12) and $v\geq 6$; and a decomposition into tight 9-cycles exists for all $v\geq 9$ divisible by 3. These results are complementary to the theorems of Akin et al. [Discrete Math. 345 (2022)] and Bunge et al. [Australas. J. Combin. 80 (2021)]. |
| title | Spectrum of $3$-uniform $6$- and $9$-cycle systems over $K_v^{(3)}-I$ |
| topic | Combinatorics 05C65, 05C51, 05C38 |
| url | https://arxiv.org/abs/2212.11058 |