Degree-balanced decompositions of cubic graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910936345870336 |
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| author | Lužar, Borut Przybyło, Jakub Soták, Roman |
| author_facet | Lužar, Borut Przybyło, Jakub Soták, Roman |
| contents | We show that every cubic graph on $n$ vertices contains a spanning subgraph in which the number of vertices of each degree deviates from $\frac{n}{4}$ by at most $\frac{1}{2}$, up to three exceptions. This resolves the conjecture of Alon and Wei (Irregular subgraphs, Combin. Probab. Comput. 32(2) (2023), 269--283) for cubic graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degree-balanced decompositions of cubic graphs Lužar, Borut Przybyło, Jakub Soták, Roman Combinatorics Discrete Mathematics 05C07 We show that every cubic graph on $n$ vertices contains a spanning subgraph in which the number of vertices of each degree deviates from $\frac{n}{4}$ by at most $\frac{1}{2}$, up to three exceptions. This resolves the conjecture of Alon and Wei (Irregular subgraphs, Combin. Probab. Comput. 32(2) (2023), 269--283) for cubic graphs. |
| title | Degree-balanced decompositions of cubic graphs |
| topic | Combinatorics Discrete Mathematics 05C07 |
| url | https://arxiv.org/abs/2408.16121 |