On distance constrained labeling of disk graphs

Authors:
Jiří Fiala;Aleksei V. Fishkin;Fedor Fomin
Affiliations:
Charles University, Faculty of Mathematics and Physics, Institute for Theoretical Computer Science (ITI), Malostranske namesti 2/25, 118 00 Prague, Czech Republic;University of Kiel, Institute for Computer Science and Applied Mathematics, Olshausenstr. 40, 24118 Kiel, Germany;Department of Informatics, University of Bergen, N-5020 Bergen, Norway
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

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.