Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
A special planar satisfiability problem and a consequence of its NP-completeness
Discrete Applied 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
Coloring precolored perfect graphs
Journal of Graph Theory
Assigning codes in wireless networks: bounds and scaling properties
Wireless Networks
Map labeling and its generalizations
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Fixed parameter complexity of λ-labelings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Distance Constrained Labeling of Precolored Trees
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Geometric Systems of Disjoint Representatives
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Graph labeling and radio channel assignment
Journal of Graph Theory
Hall's theorem for hypergraphs
Journal of Graph Theory
Approximating largest convex hulls for imprecise points
Journal of Discrete Algorithms
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We introduce a new notion of Systems of Distant Representatives of families of subsets of a metric space. We are in particular interested in the computational complexity of deciding the existence of such systems, for different distance parameters and for various metric spaces. The problem contains as a subproblem the well known polynomial time solvable problem of Systems of Distinct Representatives (for discrete metric and distance parameter 1). We prove several NP-hardness results, e.g., for discrete metric and distance parameter 2, or for Euclidean metric spaces. We also show a direct connection to practically motivated and previously studied problems such as scheduling, distance constrained graph labeling, map labeling, disjoint representatives of hypergraphs and independent sets in graphs. Finally, we mention our original motivation for studying distant representatives which comes from the distance constrained graph labeling and our complexity results imply a significant difference in the computational complexity of L(p, q)-labeling of trees for q = 1 and q 1.