Reconstructing Graphs from Connected Triples

Autor:	Bastide, Paul, Cook, Linda, Erickson, Jeff, Groenland, Carla, van Kreveld, Marc, Mannens, Isja, Vermeulen, Jordi L.
Rok vydání:	2023
Předmět:	Computer Science - Discrete Mathematics Mathematics - Combinatorics 05 G.2.2 F.2.2 G.2.1
Druh dokumentu:	Working Paper
Popis:	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 $k$. Comment: 20 pages including appendices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.06609 Zobrazit plný text záznamu View this record from Arxiv