The vertex reconstruction conjecture states that a graph on n>2 vertices can be discovered from only knowing its proper induced subgraphs.
Kelly proved this for trees in 1961. I saw his proof and I was asking the question: is his original proof still the only or simplest out there?
Actually, I found this survey by Bondy and Hemminger: "Graph Reconstruction: A Survey", where they give a significantly smaller proof on trees using a "Counting Lemma" generalising "Kelly's Lemma".