James Cruickshank, Fatemeh Mohammadi, Harshit J. Motwani, Anthony Nixon, Shin-ichi Tanigawa
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Abstract
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 743-763, March 2024. Abstract. We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in [math]. In our setting, we allow multiple vertices to be constrained to the same line. We give a combinatorial characterization of generic rigidity in this setting for arbitrary line sets. Further, under a mild assumption on the given set of lines, we give a complete combinatorial characterization of graphs that are generically globally rigid. This gives a [math]-dimensional extension of the well-known combinatorial characterization of two-dimensional global rigidity. In particular, our results imply that global rigidity is a generic property in this setting.
期刊介绍：
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.
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