Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648168 | Discrete Mathematics | 2011 | 11 Pages |
Abstract
A celebrated result of Thomassen states that not only can every planar graph be colored properly with five colors, but no matter how arbitrary palettes of five colors are assigned to vertices, one can choose a color from the corresponding palette for each vertex so that the resulting coloring is proper. This result is referred to as 5-choosability of planar graphs. Albertson asked whether Thomassen’s theorem can be extended by precoloring some vertices which are at a large enough distance apart in a graph. Here, among others, we answer the question in the case when the graph does not contain short cycles separating precolored vertices and when there is a “wide” Steiner tree containing all the precolored vertices.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Maria Axenovich, Joan P. Hutchinson, Michelle A. Lastrina,