Graded sparse graphs and body-length-direction frameworks
نویسندگان
چکیده
منابع مشابه
Bounded Direction-Length Frameworks
A direction-length framework is a pair (G, p), where G = (V ;D,L) is a ‘mixed’ graph whose edges are labeled as ‘direction’ or ‘length’ edges, and p is a map from V to R for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show t...
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Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graph...
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A two-dimensional direction-length framework is a pair (G, p), where G = (V ;D,L) is a graph whose edges are labeled as ‘direction’ or ‘length’ edges, and a map p from V to R. The label of an edge uv represents a direction or length constraint between p(u) and p(v). The framework (G, p) is called globally rigid if every other framework (G, q) in which the direction or length between the endvert...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2014.10.010