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Graphs with Flexible Labelings

  • Georg Grasegger
  • Jan Legerský
  • Josef Schicho
Article
  • 67 Downloads

Abstract

For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings, possibly non-generic. The characterization is based on colorings of the edges with restrictions on the cycles. Furthermore, we give necessary criteria and sufficient ones for the existence of such colorings.

Keywords

Graph realization Flexibility Rigidity Linkage Laman graph 

Mathematics Subject Classification

51K99 70B99 05C78 

Notes

Acknowledgements

This Project has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant Agreement No. 675789. Partially supported by the Austrian Science Fund (FWF): P26607, W1214-N15 (Project DK9); and by the Upper Austrian Government.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria
  2. 2.Research Institute for Symbolic Computation (RISC)Johannes Kepler University LinzLinzAustria

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