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

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. © 2006 Elsevier B.V. All rights reserved. MSC: 05C15; 05C78

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Baogang Xu, Haihui Zhang
• Keywords: DAM 2007, Plane Graphs, Structural Theorem, Toroidal Graph