A constructive solution to the Oberwolfach Problem with a large cycle
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915979869552640 |
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| author | Traetta, Tommaso |
| author_facet | Traetta, Tommaso |
| contents | For every $2$-regular graph $F$ of order $v$, the Oberwolfach problem $OP(F)$ asks whether there is a $2$-factorization of $K_v$ ($v$ odd) or $K_v$ minus a $1$-factor ($v$ even) into copies of $F$. Posed by Ringel in 1967 and extensively studied ever since, this problem is still open. In this paper we construct solutions to $OP(F)$ whenever $F$ contains a cycle of length greater than an explicit lower bound. Our constructions combine the amalgamation-detachment technique with methods aimed at building $2$-factorizations with an automorphism group having a nearly-regular action on the vertex-set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12713 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A constructive solution to the Oberwolfach Problem with a large cycle Traetta, Tommaso Combinatorics 05C51, 05C70, 05C15 For every $2$-regular graph $F$ of order $v$, the Oberwolfach problem $OP(F)$ asks whether there is a $2$-factorization of $K_v$ ($v$ odd) or $K_v$ minus a $1$-factor ($v$ even) into copies of $F$. Posed by Ringel in 1967 and extensively studied ever since, this problem is still open. In this paper we construct solutions to $OP(F)$ whenever $F$ contains a cycle of length greater than an explicit lower bound. Our constructions combine the amalgamation-detachment technique with methods aimed at building $2$-factorizations with an automorphism group having a nearly-regular action on the vertex-set. |
| title | A constructive solution to the Oberwolfach Problem with a large cycle |
| topic | Combinatorics 05C51, 05C70, 05C15 |
| url | https://arxiv.org/abs/2306.12713 |