Decomposition of toroidal graphs without some subgraphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916630854893568 |
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| author | Wang, Tao Yang, Xiaojing |
| author_facet | Wang, Tao Yang, Xiaojing |
| contents | We consider a family of toroidal graphs, denoted by $\mathcal{T}_{i, j}$, which contain neither $i$-cycles nor $j$-cycles. A graph $G$ is $(d, h)$-decomposable if it contains a subgraph $H$ with $Δ(H) \leq h$ such that $G - E(H)$ is a $d$-degenerate graph. For each pair $(i, j) \in \{(3, 4), (3, 6), (4, 6), (4, 7)\}$, Lu and Li proved that every graph in $\mathcal{T}_{i, j}$ is $(2, 1)$-decomposable. In this short note, we present a unified approach to prove that a common superclass of $\mathcal{T}_{i, j}$ is also $(2, 1)$-decomposable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18945 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposition of toroidal graphs without some subgraphs Wang, Tao Yang, Xiaojing Combinatorics 05C10 We consider a family of toroidal graphs, denoted by $\mathcal{T}_{i, j}$, which contain neither $i$-cycles nor $j$-cycles. A graph $G$ is $(d, h)$-decomposable if it contains a subgraph $H$ with $Δ(H) \leq h$ such that $G - E(H)$ is a $d$-degenerate graph. For each pair $(i, j) \in \{(3, 4), (3, 6), (4, 6), (4, 7)\}$, Lu and Li proved that every graph in $\mathcal{T}_{i, j}$ is $(2, 1)$-decomposable. In this short note, we present a unified approach to prove that a common superclass of $\mathcal{T}_{i, j}$ is also $(2, 1)$-decomposable. |
| title | Decomposition of toroidal graphs without some subgraphs |
| topic | Combinatorics 05C10 |
| url | https://arxiv.org/abs/2502.18945 |