Convex Polygon Intersection Graphs
نویسندگان
چکیده
Geometric intersection graphs are graphs determined by the intersections of certain geometric objects. We study the complexity of visualizing an arrangement of objects that induces a given intersection graph. We give a general framework for describing classes of geometric intersection graphs, using arbitrary finite base sets of rationally given convex polygons and rationally-constrained affine transformations as similarity maps. We prove that for every class of intersection graphs that fits this framework, the graphs in this class have a representation in integers using only polynomially many bits. Consequently, the recognition problem of these classes is in NP (and thus usually NP-complete). We also give an exponential algorithm to find suitable plane representations (‘drawings’), if a graph class fits the framework.
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