Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
420280 | Discrete Applied Mathematics | 2010 | 5 Pages |
Abstract
A polyhedral embedding in a surface is one in which any two faces have boundaries that are either disjoint or simply connected. In a cubic (3-regular) graph this is equivalent to the dual being a simple graph. In 1968, Grünbaum conjectured that every cubic graph with a polyhedral embedding in an orientable surface is 3-edge-colorable. For the sphere, this is equivalent to the Four-Color Theorem, but we have disproved the conjecture in the general form. In this paper we extend this result and show that if we restrict our attention to a class of cubic graphs with a polyhedral embedding in an orientable surface, then the computational complexity of the 3-edge-coloring problem and its approximation does not improve.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Martin Kochol,