Combinatorial Rigidity Theory for Symmetric Molecular Structures

• Project/Area Number: 24740058
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University
• Principal Investigator: TANIGAWA Shinichi 京都大学, 数理解析研究所, 助教 (30623540)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 組合せ剛性理論 / 分子構造 / グラフの剛性 / 剛性マトロイド / 群ラベル付きグラフ / 計数マトロイド / 大域剛性 / 群ラベルグラフ / 離散数学 / マトロイド / グラフ / 剛性理論

Outline of Final Research Achievements

Toward a combinatorial characterization of the global rigidity of symmetric molecular graphs, in this project we have developed new techniques for analyzing the infinitesimal rigidity of symmetric graphs and the global rigidity in high dimensional space.

Research Products

• [Int'l Joint Research] Eotvos University(Hungary)
• [Journal Article] Gain-sparsity and symmetry-forced rigidity in the plane (2016)
  • Author(s): Tibor Jordan, Viktoria Kaszanitzky, and Shin-ichi Tanigawa
  • Journal Title: Discrete & Computational Geometry Volume: 55 Issue: 2 Pages: 314-372
  • DOI: 10.1007/s00454-015-9755-1
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Count matroids of group-labeled graphs (2015)
  • Author(s): Ritanro Ikeshita and Shin-ichi Tanigawa
  • Journal Title: arXiv Volume: 1507.01259 Pages: 1-16
  • Open Access / Acknowledgement Compliant
• [Journal Article] Linking rigid bodies symmetrically (2014)
  • Author(s): Bernd Schulze and Shin-ichi Tanigawa
  • Journal Title: Eur. J. Comb. Volume: 42 Pages: 145-166
  • DOI: 10.1016/j.ejc.2014.06.002
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Generic global rigidity of body-hinge frameworks (2014)
  • Author(s): Tibor Jordan, Csaba Kiraly and Shin-ichi Tanigawa
  • Journal Title: EGRES Technical Reports Volume: TR2014-06 Pages: 1-17
• [Journal Article] Sufficient conditions for globally rigidity of graphs (2014)
  • Author(s): Shin-ichi Tanigawa
  • Journal Title: arXiv Volume: 1403.3742 Pages: 1-19
  • NAID: 120005669320
• [Journal Article] Infinitesimal rigidity of symmetric frameworks (2013)
  • Author(s): Bernd Schulze and Shin-ichi Tanigawa
  • Journal Title: arXiv Volume: 1308.6380 Pages: 1-31
• [Journal Article] Rooted-tree decompositions with matroid constraints and infinitesimal rigidity of frameworks with boundaries (2013)
  • Author(s): Naoki Katoh and Shin-ichi Tanigawa
  • Journal Title: SIAM J. Discrete Math. Volume: 27 Issue: 1 Pages: 155-185
  • DOI: 10.1137/110846944
  • Peer Reviewed
• [Journal Article] Gain-sparsity and symmetry-forced rigidity in the plane (2012)
  • Author(s): Tibor Jordan, Viktoria Kaszanitzky, Shin-ichi Tanigawa
  • Journal Title: The EGRES technical report Volume: 17 Pages: 1-66
• [Journal Article] Matroids of gain graphs in applied discrete geometry (2012)
  • Author(s): Shin-ichi Tanigawa
  • Journal Title: arXiv Volume: 1207.3601 Pages: 1-46
• [Journal Article] Periodic body-and-bar frameworks (2012)
  • Author(s): Ciprian S. Borcea, Ileana Streinu, Shin-ichi Tanigawa
  • Journal Title: Proc. 28th ACM Symposium on Computational Geometry (SoCG) Volume: 1 Pages: 347-356
  • NAID: 120005663312
  • Peer Reviewed
• [Presentation] Sparsity count on group-labeled graphs for characterizing the infinitesimal rigidity of symmetric frameworks (2015)
  • Author(s): 谷川眞一
  • Organizer: Advances in Combinatorial and Geometric Rigidity
  • Place of Presentation: バンフ（カナダ）
  • Year and Date: 2015-07-15
  • Int'l Joint Research
• [Presentation] Matroids of group-labeled graphs in graph rigidity (2015)
  • Author(s): 谷川眞一
  • Organizer: The DIAMANT symposium
  • Place of Presentation: Veenendaal（オランダ）
  • Year and Date: 2015-05-28
  • Int'l Joint Research
• [Presentation] Linking rigid bodies symmetrically (2014)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: Workshop on Geometric Structures with Symmetry and Periodicity
  • Place of Presentation: Kyoto
  • Year and Date: 2014-06-09
• [Presentation] Conditions for the unique completability of low rank positive semidefinite matrices (2014)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: Japanese-Swiss Workshop on Combinatorics and Computational Geometry
  • Place of Presentation: Tokyo
  • Year and Date: 2014-06-04
  • Invited
• [Presentation] Combinatorial conditions for the unique completability of low rank positive semidefinite matrices (2014)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: Japan Conference on Graph Theory and Combinatorics
  • Place of Presentation: Tokyo
  • Year and Date: 2014-05-17 – 2014-05-21
• [Presentation] Inductive constructions of sparse group-labeled graphs for the analysis of graph rigidity (2013)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: The 25th Workshop on Topological Graph Theory (TGT25)
  • Place of Presentation: 横浜
• [Presentation] Gain-sparsity and the rigidity of symmetric frameworks in the plane (2013)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: Joint International Meeting of the American Mathematical Society and the Romanian Mathematical Society
  • Place of Presentation: Alba Iulia, Romania
• [Presentation] Rigidity of Graphs with Symmetry (2013)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: The 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: Veszprem, Hungary
  • Invited
• [Presentation] Polymatroids of group-labeled graphs and packing non-zero A-paths (2013)
  • Author(s): Shin-ichi Tanigawa
  • Organizer: Geometric and topological graph theory 2013
  • Place of Presentation: Bristol, UK
• [Presentation] Rigidity of graphs with symmetry
  • Author(s): Shin-ichi Tanigawa
  • Organizer: RIMS workshop, Discrete Convesity and Optimization
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] Matroids of group-labeled graphs in applied discrete geometry
  • Author(s): Shin-ichi Tanigawa
  • Organizer: RIMS workshop, Discrete Geometric Analysis
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] Matroids of Gain Graphs in Applied Discrete Geometry
  • Author(s): Shin-ichi Tanigawa
  • Organizer: Rigidity Theory: Progress, Applications and Key Open Problems
  • Place of Presentation: Banff（カナダ）