{"paper":{"title":"On non-even digraphs and symplectic pairs","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chjan C. Lim, David A. Schmidt","submitted_at":"1995-07-03T00:00:00Z","abstract_excerpt":"A digraph $D$ is called {\\bf noneven} if it is possible to assign weights of 0,1 to its arcs so that $D$ contains no cycle of even weight. A noneven digraph $D$ corresponds to one or more nonsingular sign patterns. Given an $n \\times n$ sign pattern $H$, a {\\bf symplectic pair} in $Q(H)$ is a pair of matrices $(A,D)$ such that $A \\in Q(H)$, $D \\in Q(H)$, and $A^T D = I$. An unweighted digraph $D$ allows a matrix property $P$ if at least one of the sign patterns whose digraph is $D$ allows $P$. Thomassen characterized the noneven, 2-connected symmetric digraphs (i.e., digraphs for which the exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507219","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"}