Article ID Journal Published Year Pages File Type
8903055 Discrete Mathematics 2018 6 Pages PDF
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 t≥k, a (k,t)-list assignment is a list assignment L where |L(v)|≥k for all vertices v and |L(u)∪L(v)|≥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
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