{"paper":{"title":"On the Performance of the Depth First Search Algorithm in Supercritical Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Michael Krivelevich, Sahar Diskin","submitted_at":"2021-11-14T13:56:20Z","abstract_excerpt":"We consider the performance of the Depth First Search (DFS) algorithm on the random graph $G\\left(n,\\frac{1+\\epsilon}{n}\\right)$, $\\epsilon>0$ a small constant. Recently, Enriquez, Faraud and M\\'enard [2] proved that the stack $U$ of the DFS follows a specific scaling limit, reaching the maximal height of $(1+o_{\\epsilon}(1))\\epsilon^2n$. Here we provide a simple analysis for the typical length of a maximum path discovered by the DFS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07345","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.07345/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}