{"paper":{"title":"Spectral conditions for $k$-extendability and $k$-factors of bipartite graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dandan Fan, Huiqiu Lin","submitted_at":"2022-11-17T02:45:09Z","abstract_excerpt":"Let $G$ be a connected graph. If $G$ contains a matching of size $k$, and every matching of size $k$ is contained in a perfect matching of $G$, then $G$ is said to be \\emph{$k$-extendable}. A $k$-regular spanning subgraph of $G$ is called a \\textit{$k$-factor}. In this paper, we provide spectral conditions for a (balanced bipartite) graph with minimum degree $\\delta$ to be $k$-extendable, and for the existence of a $k$-factor in a balanced bipartite graph, respectively. Our results generalize some previous results on perfect matchings of graphs, and extend the results in \\cite{D.F} and \\cite{W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09304","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.09304/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"}