{"paper":{"title":"Bipartite graphs with the double Hall property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guantao Chen, Jennifer Vandenbussche, Mikhail Lavrov, Yimo Su, Yuying Ma","submitted_at":"2025-02-15T20:51:56Z","abstract_excerpt":"The super-neighborhood of a vertex set $A$ in a graph $G$, denoted by $\\Lambda^2(A)$, is the set of vertices adjacent to at least two vertices in $A$. We say that a bipartite graph $G=(X, Y)$ with $|X| \\geq 2$ satisfies the double Hall property (with respect to $X$) if $|\\Lambda^2(A)| \\geq |A|$ for any subset $A \\subseteq X$ with $|A| \\geq 2$. Kostochka et al. first conjectured that if a bipartite graph $G=(X, Y)$ satisfies a slightly weaker version of the double Hall property, then $G$ contains a cycle that covers all vertices of $X$. They verified their conjecture for $|X| \\leq 6$. In this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10903","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.10903/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"}