Edge Reconstruction Conjecture
Conjecture
Every simple graph with at least 4 edges is reconstructible from it's edge deleted subgraphs
It is known that if a graph is vertex reconstructible then it is edge reconstructible.
Bibliography
J.A.Bondy, A graph reconstruction manual, Surveys in Combinatorics, LMS-Lecture Note Series 166(1991)
* indicates original appearance(s) of problem.