A competitive algorithm to find all defective edges in a graph

Recently, Johann gave an algorithm to find all d defective edges in a graph assuming d=|D| is known. We give an algorithm with d unknown which requires at most d(⌈log2|E|⌉+4)+1 tests. The information-theoretic bound, knowing d, is about dlog2(|E|/d). For d fixed, our algorithm is competitive with coefficient 1.