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arXiv · 2504.03812

The Alon-Tarsi Number of Cartesian product and Corona product of Hypercube Graph and Special Graphs

Zhiguo Li·Yujia Gai·Zeling Shao
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Abstract

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.

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Zhiguo Li, Yujia Gai, Zeling Shao. 2025-04-04. The Alon-Tarsi Number of Cartesian product and Corona product of Hypercube Graph and Special Graphs. https://arxiv.org/abs/2504.03812

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