On minimum clique partition and maximum independent set on unit disk graphs and penny graphs: complexity and approximation

A graph G is a unit disk graph if it is the intersection graph of a family of unit disks in the euclidean plane. If the disks do not overlap, then G is also a unit coin graph or penny graph. In this work we establish the complexity of the minimum clique partition problem and the maximum independent set problem for penny graphs, both NP-complete, and present two approximation algorithms for finding clique partitions: a 3-approximation algorithm for unit disk graphs and a 3 2 -approximation algorithm for penny graphs.