Realizability of Delaunay triangulations
Information Processing Letters
Toughness and Delaunay triangulations
Discrete & Computational Geometry
A general approach to dominance in the plane
Journal of Algorithms
Graph-theoretical conditions for inscribability and Delaunay realizability
Discrete Mathematics
A note on large graphs of diameter two and given maximum degree
Journal of Combinatorial Theory Series B
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Proximity Drawability: a Survey
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Graphs and Digraphs, Fourth Edition
Graphs and Digraphs, Fourth Edition
Covering the Convex Quadrilaterals of Point Sets
Graphs and Combinatorics
Computational Geometry: Theory and Applications
Approximate proximity drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
Approximate proximity drawings
Computational Geometry: Theory and Applications
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In a witness rectangle graph (WRG) on vertex point set P with respect to witness point set W in the plane, two points x, y in P are adjacent whenever the open rectangle with x and y as opposite corners contains at least one point in W. WRGs are representative of a larger family of witness proximity graphs introduced in two previous papers. We study graph-theoretic properties of WRGs. We prove that any WRG has at most two non-trivial connected components. We bound the diameter of the non-trivial connected components of a WRG in both the one-component and two-component cases. In the latter case, we prove that a graph is representable as a WRG if and only if each component is a cointerval graph, thereby providing a complete characterization of WRGs of this type. We also completely characterize trees drawable as WRGs. Finally, we conclude with some related results on the number of points required to stab all the rectangles defined by a set of n points.