Discrete Mathematics - Topics on domination
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
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Robust algorithms for restricted domains
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
A parallel algorithmic version of the local lemma
Random Structures & Algorithms
A PTAS for the minimum dominating set problem in unit disk graphs
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
A robust PTAS for maximum weight independent sets in unit disk graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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A disk graph is the intersection graph of disks in the plane, and a unit disk graph is the intersection graph of unit radius disks in the plane. We give upper and lower bounds on the number of labeled unit disk and disk graphs on n vertices. We show that the number of unit disk graphs on n vertices is n^2^n@?@a(n)^n and the number of disk graphs on n vertices is n^3^n@?@b(n)^n, where @a(n) and @b(n) are @Q(1). We conjecture that there exist constants @a,@b such that the number of unit disk graphs is n^2^n@?(@a+o(1))^n and the number of disk graphs is n^3^n@?(@b+o(1))^n.