David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
Abstract. We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing...
Carl Droms, Brigitte Servatius, Herman Servatius
Abstract. The question of which groups admit planar Cayley graphs goes back over 100 years, being settled for finite groups by Maschke in 1896. Since that time, various authors have studied infinite...
The Finite Basis Extension Property and Graph Groups (2008)
Herman Servatius, Carl Droms, Brigitte Servatius
Introduction: A theorem of Marshall Hall, Jr. [5] (cf. also [2], [4]) states that if B = {h1,..., hk} is a free basis for a finitely generated subgroup H of a f.g. free group F, and if {x1,..., xn}...
A NOTE ON THE RANK OF SELF-DUAL POLYHEDRA. (2008)
Brigitte Servatius, Herman Servatius
Abstract. We examine how the symmetry of a self-dual polyhedron affects its rank, answering some questions in [4] A polyhedron P is said to be self-dual if there is an isomorphism δ: P → P ∗,...
Brigitte Servatius, Herman Servatius
Laman [4] proved that a simple graph G = (V, E) is (generically) rigid in the plane, if and only if there is a subset F of E such that
THE 2-DIMENSIONAL RIGIDITY OF CERTAIN FAMILIES OF GRAPHS (2008)
Bill Jackson, Brigitte Servatius, Herman Servatius
Abstract. Laman’s characterization of minimally rigid 2-dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and exploited by...
GENERIC AND ABSTRACT RIGIDITY Rigidity (2008)
Brigitte Servatius, Herman Servatius
We are all familiar with frameworks of rods attached at joints. A rod and joint framework gives rise to a simple mathematical model consisting of line segments in Euclidean 3-space with common...
THE LENGTH OF ELEMENTS IN FREE SOLVABLE GROUPS (2008)
Carl Droms, Jacques Lewin, Herman Servatius, Communicated Ronald Solomon
Abstract. We examine the relationship between the complexity of the word problem for a presentation and the complexity of the problem of determining the length of a shortest word equivalent to a...
HIGHER ORDER RIGIDITY- WHAT IS THE PROPER DEFINITION? (2008)
Robert Connelly, Herman Servatius
Abstract. We show that there is a bar–and–joint framework G(p) which has a configuration p in the plane such that the component of p in the space of all planar configurations of G has a cusp at...
Permutation Representations of the Symmetry Groups of Regular Hyperbolic Tessellations (2006)
Mushtaq, Qaiser, Servatius, Herman
Higman has questioned which discrete hyperbolic groups [p, q] have representations onto almost all symmetric and alternating groups. We call this property H and show that, except perhaps for finitely...
Non-crossing frameworks with non-crossing reciprocals (2004)
David Orden, G Ünter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, Walter Whiteley
Abstract. We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2004)
Ruth Haas, David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Herman Servatius, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). In this paper we prove that the opposite...
Non-crossing frameworks with non-crossing reciprocals (2003)
Orden, David, Rote, Guenter, Santos, Francisco, Servatios, Brigitte, Servatius, Herman, Whiteley, Walter
We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing frameworks...
Combinatorial pseudo-Triangulations (2003)
Orden, David, Santos, Francisco, Servatius, Brigitte, Servatius, Herman
We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudo-triangulation. This generalizes the main result of math.CO/0307347 which treats the...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2003)
Haas, Ruth, Orden, David, Rote, Guenter, Santos, Francisco, Servatius, Brigitte, Servatius, Herman, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees. In this paper we prove that the opposite...
Brigitte Servatius, Herman Servatius
Abstract. We consider the three forms of self-duality that can be exhibited by a planar graph G, map self-duality, graph self-duality and matroid selfduality. We show how these concepts are related...
A note on Gaussian graphs (1995)
John W. Kennedy, Herman Servatius
A graph is Gaussian if it is the graph of arcs and self-intersections of a closed C ∞ curve in the plane. In this note we describe a recursive characterization of 4-regular Gaussian graphs and give...
The structure of locally finite two-connected graphs (1995)
Carl Droms, Brigitte Servatius, Herman Servatius
We expand on Tutte's theory of 3-blocks for 2-connected graphs, generalizing it to apply to infinite, locally finite graphs, and giving necessary and sufficient conditions for a labeled tree to...
The structure of locally finite two-connected graphs, Electron (1995)
Carl Droms, Brigitte Servatius, Herman Servatius
We expand on Tutte’s theory of 3-blocks for 2-connected graphs, generalizing it to apply to infinite, locally finite graphs, and giving necessary and sufficient conditions for a labeled tree to be...
The structure of locally finite two-connected graphs, Electron (1995)
Carl Droms, Brigitte Servatius, Herman Servatius
We expand on Tutte’s theory of 3-blocks for 2-connected graphs, generalizing it to apply to infinite, locally finite graphs, and giving necessary and sufficient conditions for a labeled tree to be...
Permutation Representations of the Symmetry Groups of Regular Hyperbolic Tessellations (1993)
Qaiser Mushtaq, Herman Servatius
Higman has questioned which discrete hyperbolic groups [p, q] have representations onto almost all symmetric and alternating groups. We call this property 3tf and show that, except perhaps for...
Groups assembled from free and direct products (1992)
Carl Droms, Brigitte Servatius, Herman Servatius
Abstract. Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by...
Groups assembled from free and direct products (1992)
Carl Droms, Herman Servatius, Brigitte Servatius
Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by graphs. The...