Reconstructing Graphs from Connected Triples
Authors: 
Paul Bastide, Linda Cook, Jeff Erickson, Carla Groenland, Marc van Kreveld, Isja Mannens, Jordi L. VermeulenAuthors Info & Claims
Paul Bastide, Linda Cook, Jeff Erickson, Carla Groenland, Marc van Kreveld, Isja Mannens, Jordi L. VermeulenAuthors Info & ClaimsPages 16 - 29
Abstract
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.
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Jun 2023
490 pages
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.
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Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 23 September 2023
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