Year: 2024
Type: preprint
Abstract: The Harary reconstruction conjecture states that any graph with more than four edges can be uniquely reconstructed from its set of maximal edge-deleted subgraphs. In 1977, Müller verified the conjecture for graphs with $n$ vertices and $n \log_2(n)$ edges, improving on Lovás's bound of $\log(n^2-n)/4$. Here, we show that the reconstruction conjecture holds for graphs which have exactly one cycle and and three non-isomorphic subtrees.
Source: arXiv (Cornell University)
Authors: Pizzimenti, Anthony E., Rakhimov, Umarkhon
Institution: George Mason University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404395823