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arXiv · 2110.11617

The Alon-Tarsi number of Halin graphs

Zhiguo Li·Qing Ye·Zeling Shao
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Abstract

The Alon-Tarsi number of a graph $G$ is the smallest $k$ for which there is an orientation $D$ of $G$ with max outdegree $k-1$ such that the number of Eulerian subgraphs of $G$ with an even number of edges differs from the number of Eulerian subgraphs with an odd number of edges. In this paper, we obtain the Alon-Tarsi number of a Halin graph equals 4 when it is a wheel of even order and 3 otherwise.

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Zhiguo Li, Qing Ye, Zeling Shao. 2021-10-22. The Alon-Tarsi number of Halin graphs. https://arxiv.org/abs/2110.11617

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