1 research outputs found
On uniquely k-list colorable planar graphs, graphs on surfaces, and regular graphs
A graph is called uniquely k-list colorable (ULC) if there exists a
list of colors on its vertices, say ,
each of size , such that there is a unique proper list coloring of from
this list of colors. A graph is said to have property if it is not
uniquely -list colorable. Mahmoodian and Mahdian characterized all graphs
with property . For property has been studied only for
multipartite graphs. Here we find bounds on for graphs embedded on
surfaces, and obtain new results on planar graphs. We begin a general study of
bounds on for regular graphs, as well as for graphs with varying list
sizes