On the Performance of the Depth First Search Algorithm in Supercritical Random Graphs

We consider the performance of the Depth First Search (DFS) algorithm on the random graph $G\left(n,\frac{1+ε}{n}\right)$, $ε>0$ a small constant. Recently, Enriquez, Faraud and Ménard [2] proved that the stack $U$ of the DFS follows a specific scaling limit, reaching the maximal height of $(1+o_ε(1))ε^2n$. Here we provide a simple analysis for the typical length of a maximum path discovered by the DFS.

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