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

Authors:
Baogang Xu;Haihui Zhang
Affiliations:
School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China;School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China and Department of Mathematics, Huaiyin Teachers College, Huaian, China
Venue:
Discrete Applied Mathematics
Year:
2007

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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 K7 is a non-(3, 1)*-choosable toroidal graph. A linear time algorithm for producing such a coloring is presented also.