Generalized Petersen graphs are (1,3)-choosable
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917567564611584 |
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| author | Tang, Yunfang Yao, Yuting |
| author_facet | Tang, Yunfang Yao, Yuting |
| contents | A total weighting of a graph $G$ is a mapping $ϕ$ that assigns a weight to each vertex and each edge of $G$. The vertex-sum of $v \in V(G)$ with respect to $ϕ$ is $S_ϕ(v)=\sum_{e\in E(v)}ϕ(e)+ϕ(v)$. A total weighting is proper if adjacent vertices have distinct vertex-sums. A graph $G=(V,E)$ is called $(k,k')$-choosable if the following is true: If each vertex $x$ is assigned a set $L(x)$ of $k$ real numbers, and each edge $e$ is assigned a set $L(e)$ of $k'$ real numbers, then there is a proper total weighting $ϕ$ with $ϕ(y)\in L(y)$ for any $y \in V \cup E$. In this paper, we prove that the generalized Petersen graphs are $(1,3)$-choosable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07254 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Petersen graphs are (1,3)-choosable Tang, Yunfang Yao, Yuting Combinatorics A total weighting of a graph $G$ is a mapping $ϕ$ that assigns a weight to each vertex and each edge of $G$. The vertex-sum of $v \in V(G)$ with respect to $ϕ$ is $S_ϕ(v)=\sum_{e\in E(v)}ϕ(e)+ϕ(v)$. A total weighting is proper if adjacent vertices have distinct vertex-sums. A graph $G=(V,E)$ is called $(k,k')$-choosable if the following is true: If each vertex $x$ is assigned a set $L(x)$ of $k$ real numbers, and each edge $e$ is assigned a set $L(e)$ of $k'$ real numbers, then there is a proper total weighting $ϕ$ with $ϕ(y)\in L(y)$ for any $y \in V \cup E$. In this paper, we prove that the generalized Petersen graphs are $(1,3)$-choosable. |
| title | Generalized Petersen graphs are (1,3)-choosable |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.07254 |