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- William J. Lenhart, Richard Pollack, +6 authors Chee-Keng Yap
- Discrete & Computational Geometry
- 1987

The link center of a simple polygon P is the set of points x inside P at which the maximal link-distance from x to any other point in P is minimized, where the link distance between two points x, y inside P is defined as the smallest number of straight edges in a polygonal path inside P connecting x to y. We prove several geometric properties of the link… (More)

- William J. Lenhart, Sue Whitesides
- Discrete & Computational Geometry
- 1995

- Prosenjit Bose, Giuseppe Di Battista, William J. Lenhart, Giuseppe Liotta
- Graph Drawing
- 1994

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)

- Christopher Umans, William J. Lenhart
- FOCS
- 1997

A grid graph is a nite node-induced subgraph of the innnite two-dimensional integer grid. A solid grid graph is a grid graph without holes. For general grid graphs, the Hamiltonian cycle problem is known to be NP-complete. We give a polynomial-time algorithm for the Hamiltonian cycle problem in solid grid graphs, resolving a longstanding open question posed… (More)

- Prosenjit Bose, William J. Lenhart, Giuseppe Liotta
- Algorithmica
- 1996

Complete characterizations are given for those trees that can be drawn as either the relative neighborhood graph, relatively closest graph, gabriel graph or modified gabriel graph of a set of points in the plane. The characterizations give rise to linear-time algorithms for determining whether a tree has such a drawing; if such a drawing exists one can be… (More)

- Giuseppe Di Battista, William J. Lenhart, Giuseppe Liotta
- Graph Drawing
- 1994

- William J. Lenhart, Giuseppe Liotta
- Graph Drawing
- 1996

- David Bremner, William S. Evans, +6 authors Sue Whitesides
- Graph Drawing
- 2012

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)

- Vasek Chvátal, William J. Lenhart, Najiba Sbihi
- J. Comb. Theory, Ser. B
- 1990

- Vida Dujmovic, William S. Evans, +4 authors Stephen K. Wismath
- Comput. Geom.
- 2011

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)