Elsevier

Discrete Mathematics

Volume 313, Issue 23, 6 December 2013, Pages 2702-2711
Discrete Mathematics

Describing 3-paths in normal plane maps

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Abstract

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,), (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.

Keywords

Plane graph
Structural property
Normal plane map
3-path
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