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 ∗,...
COMBINATORICS AND THE RIGIDITY OF FRAMEWORKS (2008)
A wide variety of physical structures, e.g. scaffolding (rigid), or a DNA molecule (non-rigid), may be modeled as a collection of rigid rods connected to one another by idealized ball joints. For a...
2-SATISFIABILITY AND DIAGNOSING FAULTY PROCESSORS IN MASSIVELY PARALLEL COMPUTING SYSTEMS (2008)
Ansuman Bagchi, Brigitte Servatius, Weigeng Shi
Abstract. A fault diagnosis model for multiprocessor computers is proposed. Under normal operating mode each processor executes its own data. When an error occurs, the system is switched to the...
ABSTRACT AND GENERIC RIGIDITY IN THE PLANE (2008)
Sachin Patkar, Brigitte Servatius, K. V. Subrahmanyam
Abstract. We consider the concept of abstract 2–dimensional rigidity and rigidity matroid of a complete graph. This characterization is a natural extension of the characterization of graphic...
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
Applying Burnside’s lemma to a one-dimensional (2008)
Escher Problem, Doris Schattschneider, Brigitte Servatius
Our point of departure is the paper [7] in which a problem of M. C. Escher is solved using methods of contemporary combinatorics, in particular, Burnside’s lemma. Escher originally determined (by...
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...
Geometric Properties of Assur Graphs (2008)
Servatius, Brigitte, Shai, Offer, Whiteley, Walter
In our previous paper, we presented the combinatorial theory for minimal isostatic pinned frameworks - Assur graphs - which arise in the analysis of mechanical linkages. In this paper we further...
Combinatorial Characterization of the Assur Graphs from Engineering (2008)
Servatius, Brigitte, Shai, Offer, Whiteley, Walter
We introduce the idea of Assur graphs, a concept originally developed and exclusively employed in the literature of the kinematics community. The paper translates the terminology, questions, methods...
Session F3E ASSESSING THE QUALITY OF WEB-ENABLED LABORATORIES IN UNDERGRADUATE EDUCATION (2007)
Yevgen Amigud, Geoffrey Archer, Janelle Smith, Melissa Szymanski, Brigitte Servatius
access to state of the art equipment. The use of web-enabled laboratories in undergraduate education has dramatically increased over the past six years, but no criteria have been established to...
Applying Burnside's lemma to a one-dimmensional Escher problem (2006)
Pisanski, Tomaž, Schattschneider, Doris, Servatius, Brigitte
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...
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...
Planar Minimally Rigid Graphs and Pseudo-Triangulations (2003)
Ruth Haas, David Orden, Günter Rote, Francisco Santos, Brigitte Servatius, Hermann Servatius, ...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (incident to an angle larger than #). In this paper we prove that the opposite statement is...
Constraining plane configurations in cad: combinatorics of lengths and directions (1999)
Brigitte Servatius, Walter Whiteley
Abstract. Configurations of points in the plane constrained by only directions or by lengths alone lead to equivalent theories known as parallel drawings and infinitesimal rigidity of plane...
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...
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...
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...
Birigidity in the plane (1989)
Abstract. We consider the 2-dimensional generic rigidity matroid R(G) of a graph G. The notions of vertex and edge birigidity are introduced. We prove that vertex birigidity of G implies the...