Solution on strong partition of $2$-balanced regular multipartite tournaments
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866907831163158528 |
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| author | Ai, Jiangdong He, Fankang Liu, Yihang |
| author_facet | Ai, Jiangdong He, Fankang Liu, Yihang |
| contents | We call a partition of a $c$-partite tournament into tournaments of order $c$ is strong if each tournament is strongly connected. The strong partition number denoted as $ST(r)$, represents the minimum integer $c'$ such that every regular $r$-balanced $c$-partite tournament has a strong partition with $c\geq c'$. Figueroa, Montellano-Ballesteros and Olsen showed the existence of $ST(r)$ for all $r\geq 2$ and proved that $5\leq ST(2)\leq 7$. In this note, we establish that $ST(2)=6$ and we also show the unique $2$-balanced $5$-partite tournament which has no strong partition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08351 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solution on strong partition of $2$-balanced regular multipartite tournaments Ai, Jiangdong He, Fankang Liu, Yihang Combinatorics We call a partition of a $c$-partite tournament into tournaments of order $c$ is strong if each tournament is strongly connected. The strong partition number denoted as $ST(r)$, represents the minimum integer $c'$ such that every regular $r$-balanced $c$-partite tournament has a strong partition with $c\geq c'$. Figueroa, Montellano-Ballesteros and Olsen showed the existence of $ST(r)$ for all $r\geq 2$ and proved that $5\leq ST(2)\leq 7$. In this note, we establish that $ST(2)=6$ and we also show the unique $2$-balanced $5$-partite tournament which has no strong partition. |
| title | Solution on strong partition of $2$-balanced regular multipartite tournaments |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.08351 |