{"paper":{"title":"On testing single connectedness in directed graphs and some related problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Martin Dietzfelbinger, Raed Jaberi","submitted_at":"2014-12-04T12:20:41Z","abstract_excerpt":"Let $G=(V,E)$ be a directed graph with $n$ vertices and $m$ edges. The graph $G$ is called singly-connected if for each pair of vertices $v,w \\in V$ there is at most one simple path from $v$ to $w$ in $G$. Buchsbaum and Carlisle (1993) gave an algorithm for testing whether $G$ is singly-connected in $O(n^{2})$ time. In this paper we describe a refined version of this algorithm with running time $O(s\\cdot t+m)$, where $s$ and $t$ are the number of sources and sinks, respectively, in the reduced graph $G^{r}$ obtained by first contracting each strongly connected component of $G$ into one vertex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1639","kind":"arxiv","version":2},"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"}