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An Inductive Construction of Minimally Rigid Body-Hinge Simple Graphs

  • Yuya Higashikawa
  • Naoyuki Kamiyama
  • Naoki Katoh
  • Yuki Kobayashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8287)

Abstract

In this paper, we propose an inductive construction of minimally rigid body-hinge simple graphs. Inductive construction is one of well-studied topics in Combinatorics and Combinatorial Optimization. We develop an inductive construction for minimally rigid body-hinge simple graphs in d-dimension with d ≥ 3 by which we can develop a polynomial-time algorithm for enumerating all minimally rigid body-hinge simple graphs.

Keywords

Body-hinge framework Panel-hinge framework Body-hinge graph Combinatorial rigidity Rigid realization 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Yuya Higashikawa
    • 1
  • Naoyuki Kamiyama
    • 2
  • Naoki Katoh
    • 1
  • Yuki Kobayashi
    • 1
  1. 1.Graduate School of EngineeringKyoto UniversityKyotoJapan
  2. 2.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

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