The Alon-Tarsi number of two kinds of planar graphs

Zhiguo Li, Qing Ye, Zeling Shao


The Alon-Tarsi number AT(G) of a graph G is the least k for which there is an orientation D of G with max outdegree k − 1 such that the number of spanning Eulerian subgraphs of G with an even number of edges differs from the number of spanning Eulerian subgraphs with an odd number of edges. In this paper, the exact value of the Alon-Tarsi number of two kinds of planar graphs is obtained.


Alon-Tarsi number, choice number, chromatic number, Combinatorial Nullstellensatz, planar graph

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