The Alon-Tarsi number of two kinds of planar graphs - Zhiguo Li; Qing Ye; Zeling Shao (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2023)
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.