{"paper":{"title":"A note on the minimum skew rank of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Yanna Wang","submitted_at":"2012-06-15T09:24:48Z","abstract_excerpt":"The minimum skew rank $mr^{-}(\\mathbb{F},G)$ of a graph $G$ over a field $\\mathbb{F}$ is the smallest possible rank among all skew symmetric matrices over $\\mathbb{F}$, whose ($i$,$j$)-entry (for $i\\neq j$) is nonzero whenever $ij$ is an edge in $G$ and is zero otherwise. We give some new properties of the minimum skew rank of a graph, including a characterization of the graphs $G$ with cut vertices over the infinite field $\\mathbb{F}$ such that $mr^{-}(\\mathbb{F},G)=4$, determination of the minimum skew rank of $k$-paths over a field $\\mathbb{F}$, and an extending of an existing result to sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3409","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"}