  In an article published in 1987 in Combinatorica \cite{MR918397}, Frieze and
Jackson established a lower bound on the length of the longest induced path
(and cycle) in a sparse random graph. Their bound is obtained through a rough
analysis of a greedy algorithm. In the present work, we provide a sharp
asymptotic for the length of the induced path constructed by their algorithm.
To this end, we introduce an alternative algorithm that builds the same induced
path and whose analysis falls into the framework of a previous work by the
authors on depth-first exploration of a configuration model \cite{EFMN}. We
also analyze an extension of our algorithm that mixes depth-first and
breadth-first explorations and generates $m$-induced paths.
