Discrete Mathematics - Topics on domination
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
On the size of graphs labeled with condition at distance two
Journal of Graph Theory
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Representing graphs by disks and balls (a survey of recognition-complexity results)
Discrete Mathematics
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Fixed-Parameter Complexity of lambda-Labelings
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Robust algorithms for restricted domains
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Graph labeling and radio channel assignment
Journal of Graph Theory
A tight bound for online coloring of disk graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
A general framework for coloring problems: old results, new results, and open problems
IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory
Independence and coloring problems on intersection graphs of disks
Efficient Approximation and Online Algorithms
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A disk graph is the intersection graph of a set of disks in the plane. We consider the problem of assigning labels to vertices of a disk graph satisfying a sequence of distance constrains. Our objective is to minimize the distance between the smallest and the largest labels. We propose an on-line labeling algorithm on disk graphs, if the maximum and minimum diameters are bounded. We give the upper and lower bounds on its competitive ratio, and show that the algorithm is asymptotically optimal. In more detail we explore the case of distance constraints (2; 1), and present two off-line approximation algorithms. The last one we call robust, i.e. it does not require the disks representation and either outputs a feasible labeling, or answers the input is not a unit disk graph.