The Alon-Tarsi Number of Cartesian product and Corona product of Hypercube Graph and Special Graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913777777115136 |
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| author | Li, Zhiguo Gai, Yujia Shao, Zeling |
| author_facet | Li, Zhiguo Gai, Yujia Shao, Zeling |
| contents | The \emph{Alon-Tarsi number} of a graph $G$ is the smallest $k$ so that there exists an orientation $D$ of $G$ with max outdegree $k-1$ satisfying the number of even Eulerian subgraphs different from the number of odd Eulerian subgraphs. In this paper, the Alon-Tarsi number of the $n$-cube is obtained according to its special properties, we obtain the Alon-Tarsi number of Cartesian product of some special bipartite graphs, and get the Alon-Tarsi number of Corona product of graphs. As corollaries, we get the Alon-Tarsi number of Cartesian product and Corona product of hypercube graph and special graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Alon-Tarsi Number of Cartesian product and Corona product of Hypercube Graph and Special Graphs Li, Zhiguo Gai, Yujia Shao, Zeling Combinatorics 05C15 The \emph{Alon-Tarsi number} of a graph $G$ is the smallest $k$ so that there exists an orientation $D$ of $G$ with max outdegree $k-1$ satisfying the number of even Eulerian subgraphs different from the number of odd Eulerian subgraphs. In this paper, the Alon-Tarsi number of the $n$-cube is obtained according to its special properties, we obtain the Alon-Tarsi number of Cartesian product of some special bipartite graphs, and get the Alon-Tarsi number of Corona product of graphs. As corollaries, we get the Alon-Tarsi number of Cartesian product and Corona product of hypercube graph and special graphs. |
| title | The Alon-Tarsi Number of Cartesian product and Corona product of Hypercube Graph and Special Graphs |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2504.03812 |