Planar graphs with distance of 3-cycles at least 2 and no cycles of lengths 5, 6, 7
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909510502711296 |
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| author | Wang, Tao Wang, Ya-Nan Yang, Xiaojing |
| author_facet | Wang, Tao Wang, Ya-Nan Yang, Xiaojing |
| contents | Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of $3$-cycles at least 2 and no cycles of lengths $5, 6, 7$ are weakly $2$-degenerate. Furthermore, such graphs can be vertex-partitioned into two subgraphs, one of which has no edges, and the other is a forest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Planar graphs with distance of 3-cycles at least 2 and no cycles of lengths 5, 6, 7 Wang, Tao Wang, Ya-Nan Yang, Xiaojing Combinatorics 05C15 Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of $3$-cycles at least 2 and no cycles of lengths $5, 6, 7$ are weakly $2$-degenerate. Furthermore, such graphs can be vertex-partitioned into two subgraphs, one of which has no edges, and the other is a forest. |
| title | Planar graphs with distance of 3-cycles at least 2 and no cycles of lengths 5, 6, 7 |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2502.18090 |