William J. Lenhart

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This paper examines an innnite family of proximity drawings of graphs called open and closed-drawings, rst deened by Kirkpatrick and Radke 15, 21] in the context of computational morphology. Such proximity drawings include as special cases the well-known Gabriel, relative neighborhood and strip drawings. Complete characterizations of those trees that admit(More)
We consider contact representations of graphs where vertices are represented by cuboids, i.e. interior-disjoint axis-aligned boxes in 3D space. Edges are represented by a proper contact between the cuboids representing their end-vertices. Two cuboids make a proper contact if they intersect and their intersection is a non-zero area rectangle contained in the(More)
a r t i c l e i n f o a b s t r a c t A universal point-set supports a crossing-free drawing of any planar graph. For a planar graph with n vertices, if bends on edges of the drawing are permitted, universal point-sets of size n are known, but only if the bend points are in arbitrary positions. If the locations of the bend points must also be specified as(More)