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 (p1 ..... pk) 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 Pi, for i = 1,...,k. In the case when k = 1 and p1 = 1, this gives a traditional coloring of G. We propose and analyze several online and offiine labeling algorithms for the class of disk graphs.

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