The Alon-Tarsi number of Halin graphs
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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