{"paper":{"title":"The cover time of a biased random walk on a random regular graph of odd degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Tony Johansson","submitted_at":"2018-05-12T10:30:09Z","abstract_excerpt":"We consider a random walk process which prefers to visit previously unvisited edges, on the random $r$-regular graph $G_r$ for any odd $r\\geq 3$. We show that this random walk process has asymptotic vertex and edge cover times $\\frac{1}{r-2}n\\log n$ and $\\frac{r}{2(r-2)}n\\log n$, respectively, generalizing the result from Cooper, Frieze and Johansson from $r = 3$ to any larger odd $r$. This completes the study of the vertex cover time for fixed $r\\geq 3$, with Berenbrink, Cooper and Friedetzky having previously shown that $G_r$ has vertex cover time asymptotic to $\\frac{rn}{2}$ when $r\\geq 4$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05780","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}