In the supercritical random graph on points on the line, the largest reconstructible subset is asymptotically the full size of the giant 2-core component.
Bollob´ as,The art of mathematics: Coffee time in Memphis, Cambridge University Press (2006)
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Sharp threshold for reconstructing points on the line
In the supercritical random graph on points on the line, the largest reconstructible subset is asymptotically the full size of the giant 2-core component.