Cubic bi-Cayley graphs over solvable groups are 3-edge-colorable

(Joint work with Roman Nedela)

Bi-Cayley graphs are graphs admitting a semiregular group of automorphisms with two orbits. A notable cubic subclass of bi-Cayley graphs is the so-called generalized Petersen graphs. Castagna and Prins proved in 1972 that all generalized Petersen graphs except for the Petersen graph itself can be properly 3-edge-colored. In this talk, we are going to discuss the extension of this result to all connected cubic bi-Cayley graphs over solvable groups. Our theorem is a bi-Cayley analogue of similar results obtained by Nedela and Škoviera for Cayley graphs any by Potočnik for vertex-transitive graphs.