On uniqueness of packing of three copies of 2-factors
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909139799638016 |
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| author | Grzelec, Igor Madaras, Tomáš Onderko, Alfréd |
| author_facet | Grzelec, Igor Madaras, Tomáš Onderko, Alfréd |
| contents | The packing of three copies of a graph $G$ is the union of three edge-disjoint copies (with the same vertex set) of $G$. In this paper, we completely solve the problem of the uniqueness of packing of three copies of 2-regular graphs. In particular, we show that $C_3,C_4,C_5,C_6$ and $2C_3$ have no packing of three copies, $C_7,C_8,C_3 \cup C_4, C_4 \cup C_4, C_3 \cup C_5$ and $3C_3$ have unique packing, and any other collection of cycles has at least two distinct packings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On uniqueness of packing of three copies of 2-factors Grzelec, Igor Madaras, Tomáš Onderko, Alfréd Combinatorics 05c70 The packing of three copies of a graph $G$ is the union of three edge-disjoint copies (with the same vertex set) of $G$. In this paper, we completely solve the problem of the uniqueness of packing of three copies of 2-regular graphs. In particular, we show that $C_3,C_4,C_5,C_6$ and $2C_3$ have no packing of three copies, $C_7,C_8,C_3 \cup C_4, C_4 \cup C_4, C_3 \cup C_5$ and $3C_3$ have unique packing, and any other collection of cycles has at least two distinct packings. |
| title | On uniqueness of packing of three copies of 2-factors |
| topic | Combinatorics 05c70 |
| url | https://arxiv.org/abs/2403.11721 |