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We show that the profile of the tree constructed by the depth first search algorithm in the giant component of an Erdős‐Rényi graph with  N  vertices and connection probability  c / N  with  c  > 1 converges to an explicit deterministic shape. This makes it possible to exhibit a long nonintersecting path of lengthρ    c    −Li    2    (    ρ    c    )    c×  N  , where  ρ   c   is the density of the giant component and Li 2  denotes the dilogarithm function.

Limiting shape of the depth first search tree in an Erdős‐Rényi graph