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A Minmax Relationship Between Embeddable and Rigid Graphs by T.S. Tay; J. Nievergelt is a Mathematics article available to read on EtoBox.

What is A Minmax Relationship Between Embeddable and Rigid Graphs about?

Weighted graphs that can be embedded in Euclidean space in such a way as to preserve the weight of an edge as the distance between its two end points are of interest in a variety of applications. The concept of elastic embeddability, introduced in [1], is designed to deal with distances subject to error. Elastic graphs are related to, but distinct from, generically rigid graphs known in structural engineering. Whereas rigidity is defined via the possible motions of vertices that leave edge lengths invariant, elasticity deals with the behavior of embeddings as edge lengths are perturbed. Although these two classes are nearly disjoint, we prove that they meet at a common boundary: a graph is maximal with respect to elastic embedding if and only if it is minimal with respect to infinitesimal rigidity.

Who reads A Minmax Relationship Between Embeddable and Rigid Graphs?

Author

T.S. Tay; J. Nievergelt

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0893-9659)

Published

1997

Language

EN

Field

Mathematics (Physical Sciences)