Choosability with union separation
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 , a -list assignment is a list assignment where for all vertices and for all edges . A graph is -choosable if there is a proper coloring for every -list assignment. We explore this concept through examples of graphs that are not -choosable, demonstrating sparsity conditions that imply a graph is -choosable, and proving that all planar graphs are -choosable and -choosable.
Cite
@article{arxiv.1512.07847,
title = {Choosability with union separation},
author = {Mohit Kumbhat and Kevin Moss and Derrick Stolee},
journal= {arXiv preprint arXiv:1512.07847},
year = {2015}
}
Comments
10 pages, 2 figures