Choosability with union separation
نویسندگان
چکیده
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.
منابع مشابه
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 341 شماره
صفحات -
تاریخ انتشار 2018