Describing 3-paths in normal plane maps

作者：Borodin O V^*; Ivanova A O; Jensen T R; Kostochka A V; Yancey M P

来源：Discrete Mathematics, 2013, 313(23): 2702-2711.

DOI：10.1016/j.disc.2013.08.018

• Plane graph
• Structural property
• Normal plane map
• 3-path
• Weight

We prove that every normal plane map, as well as every 3-polytope, has a path on three vertices whose degrees are bounded from above by one of the following triplets: (3, 3, infinity), (3, 4, 11), (3, 7, 5), (3, 10, 4), (3, 15, 3), (4, 4, 9), (6, 4, 8), (7, 4, 7), and (6, 5, 6). No parameter of this description can be improved, as shown by appropriate 3-polytopes.

• 出版日期2013-12-6