Alon–Tarsi Number and Modulo Alon–Tarsi Number of Signed Graphs

We extend the concept of the Alon–Tarsi number for unsigned graph to signed one. Moreover, we introduce the modulo Alon–Tarsi number for a prime number p . We show that both the Alon–Tarsi number and modulo Alon–Tarsi number of a signed planar graph ( G , σ ) are at most 5, where the former result generalizes Zhu’s result for unsigned case and the latter one implies that ( G , σ ) is Z 5 -colorable.