On distance constrained labeling of disk graphs

A disk graph is the intersection graph of a set of disks in the plane. For a k-tuple (p(1),..., P-k) of positive integers, a distance constrained labeling of a graph G is an assignment of labels to the vertices of G such that the labels of any pair of vertices at graph distance i in G differ by at least p(i), for i = 1,..., k. In the case when k = 1 and p(1) = 1, this gives a traditional coloring of G. We propose and analyze several online and offline labeling algorithms for the class of disk graphs. (C) 2004 Elsevier B.V. All rights reserved.