Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903055 | Discrete Mathematics | 2018 | 6 Pages |
Abstract
List coloring generalizes graph coloring by requiring the color of a vertex to be selected from a list of colors specific to that vertex. One refinement of list coloring, called choosability with separation, requires that the intersection of adjacent lists is sufficiently small. We introduce a new refinement, called choosability with union separation, where we require that the union of adjacent lists is sufficiently large. For tâ¥k, a (k,t)-list assignment is a list assignment L where |L(v)|â¥k for all vertices v and |L(u)âªL(v)|â¥t for all edges uv. A graph is (k,t)-choosable if there is a proper coloring for every (k,t)-list assignment. We explore this concept through examples of graphs that are not (k,t)-choosable, demonstrating sparsity conditions that imply a graph is (k,t)-choosable, and proving that all planar graphs are (3,11)-choosable and (4,9)-choosable.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Mohit Kumbhat, Kevin Moss, Derrick Stolee,