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

- 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)

- 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)

- 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)

- 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)

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

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

Article history: Received 14 October 2011 Accepted 27 March 2012 Available online xxxx Communicated by D. Wagner

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

We show that there are, up to a trivial equivalence, precisely six theorems of the following form: If the vertices of a graph G are coloured red and white in such a way that no chordless path with four vertices is coloured in certain ways (specified by the particular theorem), then G is perfect if and only if each of the two subgraphs of G induced by all… (More)

- William S. Evans, Michael Kaufmann, William J. Lenhart, Tamara Mchedlidze, Stephen K. Wismath
- J. Graph Algorithms Appl.
- 2014

- William J. Lenhart, Giuseppe Liotta
- Inf. Process. Lett.
- 1996