Every toroidal graph without adjacent triangles is (4,1)*-choosable

AbstractIn this paper, a structural theorem about toroidal graphs is given that strengthens a result of Borodin on plane graphs. As a consequence, it is proved that every toroidal graph without adjacent triangles is (4,1)*-choosable. This result is best possible in the sense that K7 is a non-(3,1)*-choosable toroidal graph. A linear time algorithm for producing such a coloring is presented also