TY - GEN

T1 - Reconstructing Graphs from Connected Triples

AU - Mannens, Isja

AU - Groenland, Carla

AU - Kreveld, Marc van

AU - Bastide, Paul

AU - Cook, Linda

AU - Erickson, Jeff

AU - Vermeulen, Jordi Luca

PY - 2023

Y1 - 2023

N2 - We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set of connected triples, making unique reconstruction of the original graph from the triples impossible. We identify some families of graphs (including triangle-free graphs) for which all graphs have a different set of connected triples. We also give algorithms that reconstruct a graph from a set of triples, and for testing if this reconstruction is unique. Finally, we study a possible extension of the model in which the subsets of size k that induce a connected graph are given for larger (fixed) values of k.

AB - We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set of connected triples, making unique reconstruction of the original graph from the triples impossible. We identify some families of graphs (including triangle-free graphs) for which all graphs have a different set of connected triples. We also give algorithms that reconstruct a graph from a set of triples, and for testing if this reconstruction is unique. Finally, we study a possible extension of the model in which the subsets of size k that induce a connected graph are given for larger (fixed) values of k.

U2 - 10.48550/arXiv.2303.06609

DO - 10.48550/arXiv.2303.06609

M3 - Conference contribution

BT - WG 2023, Fribourg, Switzerland, 28/06/23

ER -