Graphs with Flexible Labelings
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.
KeywordsGraph realization Flexibility Rigidity Linkage Laman graph
Mathematics Subject Classification51K99 70B99 05C78
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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