Computing the extreme distances between two convex polygons
Journal of Algorithms
Representations of planar graphs
SIAM Journal on Discrete Mathematics
A special planar satisfiability problem and a consequence of its NP-completeness
Discrete Applied 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
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
Intersection Graphs of Noncrossing Arc-Connected Sets in the Plane
GD '96 Proceedings of the Symposium on Graph Drawing
Algorithmic aspects of constrained unit disk graphs
Algorithmic aspects of constrained unit disk graphs
A note on tolerance graph recognition
Discrete Applied Mathematics
Max-tolerance graphs as intersection graphs: cliques, cycles, and recognition
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Unit Circular-Arc Graph Representations and Feasible Circulations
SIAM Journal on Discrete Mathematics
A note on maximum independent set and related problems on box graphs
Information Processing Letters
The number of bits needed to represent a unit disk graph
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Integer representations of convex polygon intersection graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Geometric intersection graphs are graphs determined by intersections of geometric objects. We study the complexity of visualizing the arrangements of objects that induce such graphs. We give a general framework for describing geometric intersection graphs, using arbitrary finite base sets of rationally given convex polygons and affine transformations. We prove that for every class of intersection graphs that fits the framework, the graphs in the class have a representation using polynomially many bits. Consequently, the recognition problem of these classes is in NP (and thus NP-complete). We also give an algorithm to find a drawing of the objects in the plane, if a graph class fits the framework.