Abstract
In 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 K 7 is a non- ( 3 , 1 ) * -choosable toroidal graph. A linear time algorithm for producing such a coloring is presented also.
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