{"paper":{"title":"3-connected Reduction for Regular Graph Covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Kratochv\\'il, Ji\\v{r}\\'i Fiala, Pavel Klav\\'ik, Roman Nedela","submitted_at":"2015-03-23T08:52:13Z","abstract_excerpt":"A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular coverings in which this homomorphism is prescribed by an action of a semiregular subgroup $\\Gamma$ of $\\textrm{Aut}(G)$; so $H \\cong G / \\Gamma$. In this paper, we study the behaviour of regular graph covering with respect to 1-cuts and 2-cuts in $G$.\n  We describe reductions which produce a series of graphs $G = G_0,\\dots,G_r$ such that $G_{i+1}$ is created from $G_i$ by replacing certain inclusion minimal subgraphs with colored edges. The process ends with a primitive graph $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06556","kind":"arxiv","version":4},"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"}