We generalize the notion of online list coloring to signed graphs. We define the online list chromatic number of a signed graph, and prove a generalization of Brooks’ Theorem. We also give necessary and sufficient conditions for a signed graph to be degree paintable, or degree choosable. Finally, we classify the 2-list-colorable and 2-list-paintable signed graphs.
Tupper, M., and J. White. "Online list coloring for signed graphs." Algebra and Discrete Mathematics 33.2 (2022). https://doi.org/10.12958/adm1806
Algebra and Discrete Mathematics